KILLED proof of input_cNdiFxgsBe.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 68 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 59 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 670 ms] (16) typed CpxTrs (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (18) TRS for Loop Detection (19) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1582 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) InliningProof [UPPER BOUND(ID), 419 ms] (30) CpxRNTS (31) SimplificationProof [BOTH BOUNDS(ID, ID), 9 ms] (32) CpxRNTS (33) CompletionProof [UPPER BOUND(ID), 0 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(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) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CpxRelTRS (45) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (46) CpxTRS (47) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxWeightedTrs (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxTypedWeightedTrs (51) CompletionProof [UPPER BOUND(ID), 0 ms] (52) CpxTypedWeightedCompleteTrs (53) NarrowingProof [BOTH BOUNDS(ID, ID), 23.1 s] (54) CpxTypedWeightedCompleteTrs (55) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) InliningProof [UPPER BOUND(ID), 907 ms] (58) CpxRNTS (59) SimplificationProof [BOTH BOUNDS(ID, ID), 3 ms] (60) CpxRNTS (61) CompletionProof [UPPER BOUND(ID), 41 ms] (62) CpxTypedWeightedCompleteTrs (63) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) CdtNarrowingProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 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), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 7 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 13 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 14 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 5 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 16 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 93 ms] (188) CdtProblem (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 19 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 98 ms] (196) CdtProblem (197) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (202) CdtProblem (203) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (208) CdtProblem (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (214) CdtProblem (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 140 ms] (220) CdtProblem (221) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 20 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 162 ms] (226) CdtProblem (227) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 256 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (234) CdtProblem (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 310 ms] (236) CdtProblem (237) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 26 ms] (238) CdtProblem (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (242) CdtProblem (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (244) CdtProblem (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms] (246) CdtProblem (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (248) CdtProblem (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms] (250) CdtProblem (251) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (252) CdtProblem (253) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms] (254) CdtProblem (255) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CdtProblem (257) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms] (258) CdtProblem (259) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms] (260) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) a__U15(tt, V2) -> a__U16(a__isNat(V2)) a__U16(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) a__U22(tt, V1) -> a__U23(a__isNat(V1)) a__U23(tt) -> tt a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) a__U32(tt) -> tt a__U41(tt) -> tt a__U51(tt, N) -> a__U52(a__isNatKind(N), N) a__U52(tt, N) -> mark(N) a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) a__plus(N, 0) -> a__U51(a__isNat(N), N) a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) mark(U15(X1, X2)) -> a__U15(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U16(X)) -> a__U16(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X1, X2)) -> a__U22(mark(X1), X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X)) -> a__U41(mark(X)) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) a__isNatKind(X) -> isNatKind(X) a__U13(X1, X2, X3) -> U13(X1, X2, X3) a__U14(X1, X2, X3) -> U14(X1, X2, X3) a__U15(X1, X2) -> U15(X1, X2) a__isNat(X) -> isNat(X) a__U16(X) -> U16(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X1, X2) -> U22(X1, X2) a__U23(X) -> U23(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X) -> U41(X) a__U51(X1, X2) -> U51(X1, X2) a__U52(X1, X2) -> U52(X1, X2) a__U61(X1, X2, X3) -> U61(X1, X2, X3) a__U62(X1, X2, X3) -> U62(X1, X2, X3) a__U63(X1, X2, X3) -> U63(X1, X2, X3) a__U64(X1, X2, X3) -> U64(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, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) a__U15(tt, V2) -> a__U16(a__isNat(V2)) a__U16(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) a__U22(tt, V1) -> a__U23(a__isNat(V1)) a__U23(tt) -> tt a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) a__U32(tt) -> tt a__U41(tt) -> tt a__U51(tt, N) -> a__U52(a__isNatKind(N), N) a__U52(tt, N) -> mark(N) a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0') -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0') -> tt a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) a__plus(N, 0') -> a__U51(a__isNat(N), N) a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) mark(U15(X1, X2)) -> a__U15(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U16(X)) -> a__U16(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X1, X2)) -> a__U22(mark(X1), X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X)) -> a__U41(mark(X)) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) a__isNatKind(X) -> isNatKind(X) a__U13(X1, X2, X3) -> U13(X1, X2, X3) a__U14(X1, X2, X3) -> U14(X1, X2, X3) a__U15(X1, X2) -> U15(X1, X2) a__isNat(X) -> isNat(X) a__U16(X) -> U16(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X1, X2) -> U22(X1, X2) a__U23(X) -> U23(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X) -> U41(X) a__U51(X1, X2) -> U51(X1, X2) a__U52(X1, X2) -> U52(X1, X2) a__U61(X1, X2, X3) -> U61(X1, X2, X3) a__U62(X1, X2, X3) -> U62(X1, X2, X3) a__U63(X1, X2, X3) -> U63(X1, X2, X3) a__U64(X1, X2, X3) -> U64(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, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) a__U15(tt, V2) -> a__U16(a__isNat(V2)) a__U16(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) a__U22(tt, V1) -> a__U23(a__isNat(V1)) a__U23(tt) -> tt a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) a__U32(tt) -> tt a__U41(tt) -> tt a__U51(tt, N) -> a__U52(a__isNatKind(N), N) a__U52(tt, N) -> mark(N) a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatKind(0) -> tt a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) a__plus(N, 0) -> a__U51(a__isNat(N), N) a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) mark(U15(X1, X2)) -> a__U15(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(U16(X)) -> a__U16(mark(X)) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X1, X2)) -> a__U22(mark(X1), X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X)) -> a__U41(mark(X)) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) a__isNatKind(X) -> isNatKind(X) a__U13(X1, X2, X3) -> U13(X1, X2, X3) a__U14(X1, X2, X3) -> U14(X1, X2, X3) a__U15(X1, X2) -> U15(X1, X2) a__isNat(X) -> isNat(X) a__U16(X) -> U16(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X1, X2) -> U22(X1, X2) a__U23(X) -> U23(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X) -> U41(X) a__U51(X1, X2) -> U51(X1, X2) a__U52(X1, X2) -> U52(X1, X2) a__U61(X1, X2, X3) -> U61(X1, X2, X3) a__U62(X1, X2, X3) -> U62(X1, X2, X3) a__U63(X1, X2, X3) -> U63(X1, X2, X3) a__U64(X1, X2, X3) -> U64(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0) -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0) -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0) -> c72 S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0) -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0) -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0) -> c72 K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U15_2, A__U16_1, A__U21_2, A__U22_2, A__U23_1, A__U31_2, A__U32_1, A__U41_1, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c1, c2_2, c3, c4_2, c5, c6_2, c7, c8_2, c9, c10, c11, c12_2, c13, c14_2, c15, c16, c17, c18_2, c19, c20, c21, c22, c23, c24_2, c25, c26_1, c27, c28_2, c29, c30_2, c31, c32_2, c33, c34_2, c35_2, c36, c37, c38_2, c39_2, c40, c41, c42_2, c43_2, c44, c45_2, c46_2, c47, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c55_2, c56_2, c57_2, c58_2, c59_2, c60_2, c61_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c70, c71_1, c72 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0) -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0) -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0) -> c72 The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0') -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0') -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0') -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0') -> c72 The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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' Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0') -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0') -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0') -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0') -> c72 a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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' Types: A__U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c:c1 tt :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c :: c2:c3 -> c41:c42:c43:c44 -> c:c1 A__U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c2:c3 a__isNatKind :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 A__ISNATKIND :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c41:c42:c43:c44 c1 :: c:c1 c2 :: c4:c5 -> c41:c42:c43:c44 -> c2:c3 A__U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c4:c5 c3 :: c2:c3 c4 :: c6:c7 -> c41:c42:c43:c44 -> c4:c5 A__U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c6:c7 c5 :: c4:c5 c6 :: c8:c9 -> c37:c38:c39:c40 -> c6:c7 A__U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c8:c9 a__isNat :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 A__ISNAT :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c37:c38:c39:c40 c7 :: c6:c7 c8 :: c10:c11 -> c37:c38:c39:c40 -> c8:c9 A__U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c10:c11 c9 :: c8:c9 c10 :: c10:c11 c11 :: c10:c11 A__U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c12:c13 c12 :: c14:c15 -> c41:c42:c43:c44 -> c12:c13 A__U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c14:c15 c13 :: c12:c13 c14 :: c16:c17 -> c37:c38:c39:c40 -> c14:c15 A__U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c16:c17 c15 :: c14:c15 c16 :: c16:c17 c17 :: c16:c17 A__U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c18:c19 c18 :: c20:c21 -> c41:c42:c43:c44 -> c18:c19 A__U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c20:c21 c19 :: c18:c19 c20 :: c20:c21 c21 :: c20:c21 A__U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c22:c23 c22 :: c22:c23 c23 :: c22:c23 A__U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c24:c25 c24 :: c26:c27 -> c41:c42:c43:c44 -> c24:c25 A__U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c26:c27 c25 :: c24:c25 c26 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c26:c27 MARK :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c27 :: c26:c27 A__U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c28:c29 c28 :: c30:c31 -> c41:c42:c43:c44 -> c28:c29 A__U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c30:c31 c29 :: c28:c29 c30 :: c32:c33 -> c37:c38:c39:c40 -> c30:c31 A__U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c32:c33 c31 :: c30:c31 c32 :: c34:c35:c36 -> c41:c42:c43:c44 -> c32:c33 A__U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c34:c35:c36 c33 :: c32:c33 c34 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c34:c35:c36 A__PLUS :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c45:c46:c47 mark :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c35 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c34:c35:c36 c36 :: c34:c35:c36 0' :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c37 :: c37:c38:c39:c40 plus :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c38 :: c:c1 -> c41:c42:c43:c44 -> c37:c38:c39:c40 s :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c39 :: c12:c13 -> c41:c42:c43:c44 -> c37:c38:c39:c40 c40 :: c37:c38:c39:c40 c41 :: c41:c42:c43:c44 c42 :: c18:c19 -> c41:c42:c43:c44 -> c41:c42:c43:c44 c43 :: c22:c23 -> c41:c42:c43:c44 -> c41:c42:c43:c44 c44 :: c41:c42:c43:c44 c45 :: c24:c25 -> c37:c38:c39:c40 -> c45:c46:c47 c46 :: c28:c29 -> c37:c38:c39:c40 -> c45:c46:c47 c47 :: c45:c46:c47 U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c48 :: c:c1 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c49 :: c2:c3 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 isNatKind :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c50 :: c41:c42:c43:c44 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c51 :: c4:c5 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c52 :: c6:c7 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c53 :: c8:c9 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 isNat :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c54 :: c37:c38:c39:c40 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c55 :: c10:c11 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c56 :: c12:c13 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c57 :: c14:c15 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c58 :: c16:c17 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c59 :: c18:c19 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c60 :: c20:c21 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c61 :: c22:c23 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c62 :: c24:c25 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c63 :: c26:c27 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c64 :: c28:c29 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c65 :: c30:c31 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c66 :: c32:c33 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c67 :: c34:c35:c36 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c68 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c69 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c70 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c71 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c72 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 a__U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__plus :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 hole_c:c11_73 :: c:c1 hole_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U642_73 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 hole_c2:c33_73 :: c2:c3 hole_c41:c42:c43:c444_73 :: c41:c42:c43:c44 hole_c4:c55_73 :: c4:c5 hole_c6:c76_73 :: c6:c7 hole_c8:c97_73 :: c8:c9 hole_c37:c38:c39:c408_73 :: c37:c38:c39:c40 hole_c10:c119_73 :: c10:c11 hole_c12:c1310_73 :: c12:c13 hole_c14:c1511_73 :: c14:c15 hole_c16:c1712_73 :: c16:c17 hole_c18:c1913_73 :: c18:c19 hole_c20:c2114_73 :: c20:c21 hole_c22:c2315_73 :: c22:c23 hole_c24:c2516_73 :: c24:c25 hole_c26:c2717_73 :: c26:c27 hole_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7218_73 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 hole_c28:c2919_73 :: c28:c29 hole_c30:c3120_73 :: c30:c31 hole_c32:c3321_73 :: c32:c33 hole_c34:c35:c3622_73 :: c34:c35:c36 hole_c45:c46:c4723_73 :: c45:c46:c47 gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73 :: Nat -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 gen_c41:c42:c43:c4425_73 :: Nat -> c41:c42:c43:c44 gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73 :: Nat -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, A__U12, a__isNatKind, A__ISNATKIND, A__U13, A__U14, A__U15, a__isNat, A__ISNAT, A__U21, A__U22, A__U31, A__U51, A__U52, MARK, A__U61, A__U62, A__U63, A__U64, A__PLUS, mark, a__U11, a__U12, a__U13, a__U14, a__U15, a__U21, a__U22, a__U31, a__U51, a__U52, a__U61, a__U62, a__U63, a__U64, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNatKind < A__U11 A__ISNATKIND < A__U11 A__U11 = A__U13 A__U11 = A__U14 A__U11 = A__U15 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U22 A__U11 < MARK a__isNatKind < A__U12 A__ISNATKIND < A__U12 A__U12 = A__U13 A__U12 = A__U14 A__U12 = A__U15 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U22 A__U12 < MARK a__isNatKind < A__ISNATKIND a__isNatKind < A__U13 a__isNatKind < a__isNat a__isNatKind < A__ISNAT a__isNatKind < A__U21 a__isNatKind < A__U31 a__isNatKind < A__U51 a__isNatKind < A__U61 a__isNatKind < A__U63 a__isNatKind < mark a__isNatKind < a__U11 a__isNatKind < a__U12 a__isNatKind < a__U13 a__isNatKind < a__U21 a__isNatKind = a__U31 a__isNatKind < a__U51 a__isNatKind < a__U61 a__isNatKind < a__U63 A__ISNATKIND < A__U13 A__ISNATKIND < A__ISNAT A__ISNATKIND < A__U21 A__ISNATKIND = A__U31 A__ISNATKIND < A__U51 A__ISNATKIND < MARK A__ISNATKIND < A__U61 A__ISNATKIND < A__U63 A__U13 = A__U14 A__U13 = A__U15 A__U13 = A__ISNAT A__U13 = A__U21 A__U13 = A__U22 A__U13 < MARK A__U14 = A__U15 a__isNat < A__U14 A__U14 = A__ISNAT A__U14 = A__U21 A__U14 = A__U22 A__U14 < MARK a__isNat < A__U15 A__U15 = A__ISNAT A__U15 = A__U21 A__U15 = A__U22 A__U15 < MARK a__isNat < A__U22 a__isNat < A__U62 a__isNat < A__PLUS a__isNat < mark a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U13 a__isNat = a__U14 a__isNat = a__U15 a__isNat = a__U21 a__isNat = a__U22 a__isNat < a__U62 a__isNat < a__plus A__ISNAT = A__U21 A__ISNAT = A__U22 A__ISNAT < MARK A__ISNAT < A__U62 A__ISNAT < A__PLUS A__U21 = A__U22 A__U21 < MARK A__U22 < MARK A__U31 < MARK A__U51 = A__U52 A__U51 = MARK A__U51 = A__U61 A__U51 = A__U62 A__U51 = A__U63 A__U51 = A__U64 A__U51 = A__PLUS A__U52 = MARK A__U52 = A__U61 A__U52 = A__U62 A__U52 = A__U63 A__U52 = A__U64 A__U52 = A__PLUS MARK = A__U61 MARK = A__U62 MARK = A__U63 MARK = A__U64 MARK = A__PLUS mark < MARK A__U61 = A__U62 A__U61 = A__U63 A__U61 = A__U64 A__U61 = A__PLUS A__U62 = A__U63 A__U62 = A__U64 A__U62 = A__PLUS A__U63 = A__U64 A__U63 = A__PLUS A__U64 = A__PLUS mark < A__U64 a__U11 < mark a__U12 < mark a__U13 < mark a__U14 < mark a__U15 < mark a__U21 < mark a__U22 < mark a__U31 < mark mark = a__U51 mark = a__U52 mark = a__U61 mark = a__U62 mark = a__U63 mark = a__U64 mark = a__plus a__U11 = a__U12 a__U11 = a__U13 a__U11 = a__U14 a__U11 = a__U15 a__U11 = a__U21 a__U11 = a__U22 a__U12 = a__U13 a__U12 = a__U14 a__U12 = a__U15 a__U12 = a__U21 a__U12 = a__U22 a__U13 = a__U14 a__U13 = a__U15 a__U13 = a__U21 a__U13 = a__U22 a__U14 = a__U15 a__U14 = a__U21 a__U14 = a__U22 a__U15 = a__U21 a__U15 = a__U22 a__U21 = a__U22 a__U51 = a__U52 a__U51 = a__U61 a__U51 = a__U62 a__U51 = a__U63 a__U51 = a__U64 a__U51 = a__plus a__U52 = a__U61 a__U52 = a__U62 a__U52 = a__U63 a__U52 = a__U64 a__U52 = a__plus a__U61 = a__U62 a__U61 = a__U63 a__U61 = a__U64 a__U61 = a__plus a__U62 = a__U63 a__U62 = a__U64 a__U62 = a__plus a__U63 = a__U64 a__U63 = a__plus a__U64 = a__plus ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0') -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0') -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0') -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0') -> c72 a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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' Types: A__U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c:c1 tt :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c :: c2:c3 -> c41:c42:c43:c44 -> c:c1 A__U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c2:c3 a__isNatKind :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 A__ISNATKIND :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c41:c42:c43:c44 c1 :: c:c1 c2 :: c4:c5 -> c41:c42:c43:c44 -> c2:c3 A__U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c4:c5 c3 :: c2:c3 c4 :: c6:c7 -> c41:c42:c43:c44 -> c4:c5 A__U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c6:c7 c5 :: c4:c5 c6 :: c8:c9 -> c37:c38:c39:c40 -> c6:c7 A__U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c8:c9 a__isNat :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 A__ISNAT :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c37:c38:c39:c40 c7 :: c6:c7 c8 :: c10:c11 -> c37:c38:c39:c40 -> c8:c9 A__U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c10:c11 c9 :: c8:c9 c10 :: c10:c11 c11 :: c10:c11 A__U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c12:c13 c12 :: c14:c15 -> c41:c42:c43:c44 -> c12:c13 A__U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c14:c15 c13 :: c12:c13 c14 :: c16:c17 -> c37:c38:c39:c40 -> c14:c15 A__U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c16:c17 c15 :: c14:c15 c16 :: c16:c17 c17 :: c16:c17 A__U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c18:c19 c18 :: c20:c21 -> c41:c42:c43:c44 -> c18:c19 A__U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c20:c21 c19 :: c18:c19 c20 :: c20:c21 c21 :: c20:c21 A__U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c22:c23 c22 :: c22:c23 c23 :: c22:c23 A__U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c24:c25 c24 :: c26:c27 -> c41:c42:c43:c44 -> c24:c25 A__U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c26:c27 c25 :: c24:c25 c26 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c26:c27 MARK :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c27 :: c26:c27 A__U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c28:c29 c28 :: c30:c31 -> c41:c42:c43:c44 -> c28:c29 A__U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c30:c31 c29 :: c28:c29 c30 :: c32:c33 -> c37:c38:c39:c40 -> c30:c31 A__U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c32:c33 c31 :: c30:c31 c32 :: c34:c35:c36 -> c41:c42:c43:c44 -> c32:c33 A__U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c34:c35:c36 c33 :: c32:c33 c34 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c34:c35:c36 A__PLUS :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c45:c46:c47 mark :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c35 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c34:c35:c36 c36 :: c34:c35:c36 0' :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c37 :: c37:c38:c39:c40 plus :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c38 :: c:c1 -> c41:c42:c43:c44 -> c37:c38:c39:c40 s :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c39 :: c12:c13 -> c41:c42:c43:c44 -> c37:c38:c39:c40 c40 :: c37:c38:c39:c40 c41 :: c41:c42:c43:c44 c42 :: c18:c19 -> c41:c42:c43:c44 -> c41:c42:c43:c44 c43 :: c22:c23 -> c41:c42:c43:c44 -> c41:c42:c43:c44 c44 :: c41:c42:c43:c44 c45 :: c24:c25 -> c37:c38:c39:c40 -> c45:c46:c47 c46 :: c28:c29 -> c37:c38:c39:c40 -> c45:c46:c47 c47 :: c45:c46:c47 U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c48 :: c:c1 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c49 :: c2:c3 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 isNatKind :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c50 :: c41:c42:c43:c44 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c51 :: c4:c5 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c52 :: c6:c7 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c53 :: c8:c9 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 isNat :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c54 :: c37:c38:c39:c40 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c55 :: c10:c11 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c56 :: c12:c13 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c57 :: c14:c15 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> 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tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c67 :: c34:c35:c36 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c68 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c69 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c70 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c71 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c72 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 a__U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> 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tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__plus :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 hole_c:c11_73 :: c:c1 hole_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U642_73 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 hole_c2:c33_73 :: c2:c3 hole_c41:c42:c43:c444_73 :: c41:c42:c43:c44 hole_c4:c55_73 :: c4:c5 hole_c6:c76_73 :: c6:c7 hole_c8:c97_73 :: c8:c9 hole_c37:c38:c39:c408_73 :: c37:c38:c39:c40 hole_c10:c119_73 :: c10:c11 hole_c12:c1310_73 :: c12:c13 hole_c14:c1511_73 :: c14:c15 hole_c16:c1712_73 :: c16:c17 hole_c18:c1913_73 :: c18:c19 hole_c20:c2114_73 :: c20:c21 hole_c22:c2315_73 :: c22:c23 hole_c24:c2516_73 :: c24:c25 hole_c26:c2717_73 :: c26:c27 hole_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7218_73 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 hole_c28:c2919_73 :: c28:c29 hole_c30:c3120_73 :: c30:c31 hole_c32:c3321_73 :: c32:c33 hole_c34:c35:c3622_73 :: c34:c35:c36 hole_c45:c46:c4723_73 :: c45:c46:c47 gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73 :: Nat -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 gen_c41:c42:c43:c4425_73 :: Nat -> c41:c42:c43:c44 gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73 :: Nat -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 Generator Equations: gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(0) <=> tt gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(x), tt) gen_c41:c42:c43:c4425_73(0) <=> c41 gen_c41:c42:c43:c4425_73(+(x, 1)) <=> c42(c18(c20, c41), gen_c41:c42:c43:c4425_73(x)) gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73(0) <=> c50(c41) gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73(+(x, 1)) <=> c48(c(c2(c4(c6(c8(c10, c37), c37), c41), c41), c41), gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73(x)) The following defined symbols remain to be analysed: a__U31, A__U11, A__U12, a__isNatKind, A__ISNATKIND, A__U13, A__U14, A__U15, a__isNat, A__ISNAT, A__U21, A__U22, A__U31, A__U51, A__U52, MARK, A__U61, A__U62, A__U63, A__U64, A__PLUS, mark, a__U11, a__U12, a__U13, a__U14, a__U15, a__U21, a__U22, a__U51, a__U52, a__U61, a__U62, a__U63, a__U64, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNatKind < A__U11 A__ISNATKIND < A__U11 A__U11 = A__U13 A__U11 = A__U14 A__U11 = A__U15 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U22 A__U11 < MARK a__isNatKind < A__U12 A__ISNATKIND < A__U12 A__U12 = A__U13 A__U12 = A__U14 A__U12 = A__U15 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U22 A__U12 < MARK a__isNatKind < A__ISNATKIND a__isNatKind < A__U13 a__isNatKind < a__isNat a__isNatKind < A__ISNAT a__isNatKind < A__U21 a__isNatKind < A__U31 a__isNatKind < A__U51 a__isNatKind < A__U61 a__isNatKind < A__U63 a__isNatKind < mark a__isNatKind < a__U11 a__isNatKind < a__U12 a__isNatKind < a__U13 a__isNatKind < a__U21 a__isNatKind = a__U31 a__isNatKind < a__U51 a__isNatKind < a__U61 a__isNatKind < a__U63 A__ISNATKIND < A__U13 A__ISNATKIND < A__ISNAT A__ISNATKIND < A__U21 A__ISNATKIND = A__U31 A__ISNATKIND < A__U51 A__ISNATKIND < MARK A__ISNATKIND < A__U61 A__ISNATKIND < A__U63 A__U13 = A__U14 A__U13 = A__U15 A__U13 = A__ISNAT A__U13 = A__U21 A__U13 = A__U22 A__U13 < MARK A__U14 = A__U15 a__isNat < A__U14 A__U14 = A__ISNAT A__U14 = A__U21 A__U14 = A__U22 A__U14 < MARK a__isNat < A__U15 A__U15 = A__ISNAT A__U15 = A__U21 A__U15 = A__U22 A__U15 < MARK a__isNat < A__U22 a__isNat < A__U62 a__isNat < A__PLUS a__isNat < mark a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U13 a__isNat = a__U14 a__isNat = a__U15 a__isNat = a__U21 a__isNat = a__U22 a__isNat < a__U62 a__isNat < a__plus A__ISNAT = A__U21 A__ISNAT = A__U22 A__ISNAT < MARK A__ISNAT < A__U62 A__ISNAT < A__PLUS A__U21 = A__U22 A__U21 < MARK A__U22 < MARK A__U31 < MARK A__U51 = A__U52 A__U51 = MARK A__U51 = A__U61 A__U51 = A__U62 A__U51 = A__U63 A__U51 = A__U64 A__U51 = A__PLUS A__U52 = MARK A__U52 = A__U61 A__U52 = A__U62 A__U52 = A__U63 A__U52 = A__U64 A__U52 = A__PLUS MARK = A__U61 MARK = A__U62 MARK = A__U63 MARK = A__U64 MARK = A__PLUS mark < MARK A__U61 = A__U62 A__U61 = A__U63 A__U61 = A__U64 A__U61 = A__PLUS A__U62 = A__U63 A__U62 = A__U64 A__U62 = A__PLUS A__U63 = A__U64 A__U63 = A__PLUS A__U64 = A__PLUS mark < A__U64 a__U11 < mark a__U12 < mark a__U13 < mark a__U14 < mark a__U15 < mark a__U21 < mark a__U22 < mark a__U31 < mark mark = a__U51 mark = a__U52 mark = a__U61 mark = a__U62 mark = a__U63 mark = a__U64 mark = a__plus a__U11 = a__U12 a__U11 = a__U13 a__U11 = a__U14 a__U11 = a__U15 a__U11 = a__U21 a__U11 = a__U22 a__U12 = a__U13 a__U12 = a__U14 a__U12 = a__U15 a__U12 = a__U21 a__U12 = a__U22 a__U13 = a__U14 a__U13 = a__U15 a__U13 = a__U21 a__U13 = a__U22 a__U14 = a__U15 a__U14 = a__U21 a__U14 = a__U22 a__U15 = a__U21 a__U15 = a__U22 a__U21 = a__U22 a__U51 = a__U52 a__U51 = a__U61 a__U51 = a__U62 a__U51 = a__U63 a__U51 = a__U64 a__U51 = a__plus a__U52 = a__U61 a__U52 = a__U62 a__U52 = a__U63 a__U52 = a__U64 a__U52 = a__plus a__U61 = a__U62 a__U61 = a__U63 a__U61 = a__U64 a__U61 = a__plus a__U62 = a__U63 a__U62 = a__U64 a__U62 = a__plus a__U63 = a__U64 a__U63 = a__plus a__U64 = a__plus ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__isNatKind(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(1, n976_73))) -> *27_73, rt in Omega(0) Induction Base: a__isNatKind(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(1, 0))) Induction Step: a__isNatKind(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(1, +(n976_73, 1)))) ->_R^Omega(0) a__U31(a__isNatKind(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(1, n976_73))), tt) ->_IH a__U31(*27_73, tt) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0') -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0') -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0') -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0') -> c72 a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0') -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0') -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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' Types: A__U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c:c1 tt :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c :: c2:c3 -> c41:c42:c43:c44 -> c:c1 A__U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c2:c3 a__isNatKind :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 A__ISNATKIND :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c41:c42:c43:c44 c1 :: c:c1 c2 :: c4:c5 -> c41:c42:c43:c44 -> c2:c3 A__U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c4:c5 c3 :: c2:c3 c4 :: c6:c7 -> c41:c42:c43:c44 -> c4:c5 A__U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c6:c7 c5 :: c4:c5 c6 :: c8:c9 -> c37:c38:c39:c40 -> c6:c7 A__U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c8:c9 a__isNat :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 A__ISNAT :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c37:c38:c39:c40 c7 :: c6:c7 c8 :: c10:c11 -> c37:c38:c39:c40 -> c8:c9 A__U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c10:c11 c9 :: c8:c9 c10 :: c10:c11 c11 :: c10:c11 A__U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c12:c13 c12 :: c14:c15 -> c41:c42:c43:c44 -> c12:c13 A__U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c14:c15 c13 :: c12:c13 c14 :: c16:c17 -> c37:c38:c39:c40 -> c14:c15 A__U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c16:c17 c15 :: c14:c15 c16 :: c16:c17 c17 :: c16:c17 A__U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c18:c19 c18 :: c20:c21 -> c41:c42:c43:c44 -> c18:c19 A__U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c20:c21 c19 :: c18:c19 c20 :: c20:c21 c21 :: c20:c21 A__U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c22:c23 c22 :: c22:c23 c23 :: c22:c23 A__U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c24:c25 c24 :: c26:c27 -> c41:c42:c43:c44 -> c24:c25 A__U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c26:c27 c25 :: c24:c25 c26 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c26:c27 MARK :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 c27 :: c26:c27 A__U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c28:c29 c28 :: c30:c31 -> c41:c42:c43:c44 -> c28:c29 A__U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c30:c31 c29 :: c28:c29 c30 :: c32:c33 -> c37:c38:c39:c40 -> c30:c31 A__U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c32:c33 c31 :: c30:c31 c32 :: c34:c35:c36 -> c41:c42:c43:c44 -> c32:c33 A__U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c34:c35:c36 c33 :: c32:c33 c34 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c34:c35:c36 A__PLUS :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> c45:c46:c47 mark :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c35 :: c45:c46:c47 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c34:c35:c36 c36 :: c34:c35:c36 0' :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c37 :: c37:c38:c39:c40 plus :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c38 :: c:c1 -> c41:c42:c43:c44 -> c37:c38:c39:c40 s :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c39 :: c12:c13 -> c41:c42:c43:c44 -> c37:c38:c39:c40 c40 :: c37:c38:c39:c40 c41 :: c41:c42:c43:c44 c42 :: c18:c19 -> c41:c42:c43:c44 -> c41:c42:c43:c44 c43 :: c22:c23 -> c41:c42:c43:c44 -> c41:c42:c43:c44 c44 :: c41:c42:c43:c44 c45 :: c24:c25 -> c37:c38:c39:c40 -> c45:c46:c47 c46 :: c28:c29 -> c37:c38:c39:c40 -> c45:c46:c47 c47 :: c45:c46:c47 U11 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c48 :: c:c1 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U12 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c49 :: c2:c3 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 isNatKind :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c50 :: c41:c42:c43:c44 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U13 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c51 :: c4:c5 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U14 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c52 :: c6:c7 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U15 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c53 :: c8:c9 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 isNat :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c54 :: c37:c38:c39:c40 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U16 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c55 :: c10:c11 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U21 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c56 :: c12:c13 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U22 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c57 :: c14:c15 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U23 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c58 :: c16:c17 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c59 :: c18:c19 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c60 :: c20:c21 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 c61 :: c22:c23 -> 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tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U31 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U32 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U41 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U51 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U52 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U61 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U62 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U63 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U64 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__plus :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 hole_c:c11_73 :: c:c1 hole_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U642_73 :: tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 hole_c2:c33_73 :: c2:c3 hole_c41:c42:c43:c444_73 :: c41:c42:c43:c44 hole_c4:c55_73 :: c4:c5 hole_c6:c76_73 :: c6:c7 hole_c8:c97_73 :: c8:c9 hole_c37:c38:c39:c408_73 :: c37:c38:c39:c40 hole_c10:c119_73 :: c10:c11 hole_c12:c1310_73 :: c12:c13 hole_c14:c1511_73 :: c14:c15 hole_c16:c1712_73 :: c16:c17 hole_c18:c1913_73 :: c18:c19 hole_c20:c2114_73 :: c20:c21 hole_c22:c2315_73 :: c22:c23 hole_c24:c2516_73 :: c24:c25 hole_c26:c2717_73 :: c26:c27 hole_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7218_73 :: c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 hole_c28:c2919_73 :: c28:c29 hole_c30:c3120_73 :: c30:c31 hole_c32:c3321_73 :: c32:c33 hole_c34:c35:c3622_73 :: c34:c35:c36 hole_c45:c46:c4723_73 :: c45:c46:c47 gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73 :: Nat -> tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 gen_c41:c42:c43:c4425_73 :: Nat -> c41:c42:c43:c44 gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73 :: Nat -> c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72 Lemmas: a__isNatKind(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(1, n976_73))) -> *27_73, rt in Omega(0) Generator Equations: gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(0) <=> tt gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U6424_73(x), tt) gen_c41:c42:c43:c4425_73(0) <=> c41 gen_c41:c42:c43:c4425_73(+(x, 1)) <=> c42(c18(c20, c41), gen_c41:c42:c43:c4425_73(x)) gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73(0) <=> c50(c41) gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73(+(x, 1)) <=> c48(c(c2(c4(c6(c8(c10, c37), c37), c41), c41), c41), gen_c48:c49:c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c7226_73(x)) The following defined symbols remain to be analysed: a__U31, A__U11, A__U12, A__ISNATKIND, A__U13, A__U14, A__U15, a__isNat, A__ISNAT, A__U21, A__U22, A__U31, A__U51, A__U52, MARK, A__U61, A__U62, A__U63, A__U64, A__PLUS, mark, a__U11, a__U12, a__U13, a__U14, a__U15, a__U21, a__U22, a__U51, a__U52, a__U61, a__U62, a__U63, a__U64, a__plus They will be analysed ascendingly in the following order: A__U11 = A__U12 a__isNatKind < A__U11 A__ISNATKIND < A__U11 A__U11 = A__U13 A__U11 = A__U14 A__U11 = A__U15 A__U11 = A__ISNAT A__U11 = A__U21 A__U11 = A__U22 A__U11 < MARK a__isNatKind < A__U12 A__ISNATKIND < A__U12 A__U12 = A__U13 A__U12 = A__U14 A__U12 = A__U15 A__U12 = A__ISNAT A__U12 = A__U21 A__U12 = A__U22 A__U12 < MARK a__isNatKind < A__ISNATKIND a__isNatKind < A__U13 a__isNatKind < a__isNat a__isNatKind < A__ISNAT a__isNatKind < A__U21 a__isNatKind < A__U31 a__isNatKind < A__U51 a__isNatKind < A__U61 a__isNatKind < A__U63 a__isNatKind < mark a__isNatKind < a__U11 a__isNatKind < a__U12 a__isNatKind < a__U13 a__isNatKind < a__U21 a__isNatKind = a__U31 a__isNatKind < a__U51 a__isNatKind < a__U61 a__isNatKind < a__U63 A__ISNATKIND < A__U13 A__ISNATKIND < A__ISNAT A__ISNATKIND < A__U21 A__ISNATKIND = A__U31 A__ISNATKIND < A__U51 A__ISNATKIND < MARK A__ISNATKIND < A__U61 A__ISNATKIND < A__U63 A__U13 = A__U14 A__U13 = A__U15 A__U13 = A__ISNAT A__U13 = A__U21 A__U13 = A__U22 A__U13 < MARK A__U14 = A__U15 a__isNat < A__U14 A__U14 = A__ISNAT A__U14 = A__U21 A__U14 = A__U22 A__U14 < MARK a__isNat < A__U15 A__U15 = A__ISNAT A__U15 = A__U21 A__U15 = A__U22 A__U15 < MARK a__isNat < A__U22 a__isNat < A__U62 a__isNat < A__PLUS a__isNat < mark a__isNat = a__U11 a__isNat = a__U12 a__isNat = a__U13 a__isNat = a__U14 a__isNat = a__U15 a__isNat = a__U21 a__isNat = a__U22 a__isNat < a__U62 a__isNat < a__plus A__ISNAT = A__U21 A__ISNAT = A__U22 A__ISNAT < MARK A__ISNAT < A__U62 A__ISNAT < A__PLUS A__U21 = A__U22 A__U21 < MARK A__U22 < MARK A__U31 < MARK A__U51 = A__U52 A__U51 = MARK A__U51 = A__U61 A__U51 = A__U62 A__U51 = A__U63 A__U51 = A__U64 A__U51 = A__PLUS A__U52 = MARK A__U52 = A__U61 A__U52 = A__U62 A__U52 = A__U63 A__U52 = A__U64 A__U52 = A__PLUS MARK = A__U61 MARK = A__U62 MARK = A__U63 MARK = A__U64 MARK = A__PLUS mark < MARK A__U61 = A__U62 A__U61 = A__U63 A__U61 = A__U64 A__U61 = A__PLUS A__U62 = A__U63 A__U62 = A__U64 A__U62 = A__PLUS A__U63 = A__U64 A__U63 = A__PLUS A__U64 = A__PLUS mark < A__U64 a__U11 < mark a__U12 < mark a__U13 < mark a__U14 < mark a__U15 < mark a__U21 < mark a__U22 < mark a__U31 < mark mark = a__U51 mark = a__U52 mark = a__U61 mark = a__U62 mark = a__U63 mark = a__U64 mark = a__plus a__U11 = a__U12 a__U11 = a__U13 a__U11 = a__U14 a__U11 = a__U15 a__U11 = a__U21 a__U11 = a__U22 a__U12 = a__U13 a__U12 = a__U14 a__U12 = a__U15 a__U12 = a__U21 a__U12 = a__U22 a__U13 = a__U14 a__U13 = a__U15 a__U13 = a__U21 a__U13 = a__U22 a__U14 = a__U15 a__U14 = a__U21 a__U14 = a__U22 a__U15 = a__U21 a__U15 = a__U22 a__U21 = a__U22 a__U51 = a__U52 a__U51 = a__U61 a__U51 = a__U62 a__U51 = a__U63 a__U51 = a__U64 a__U51 = a__plus a__U52 = a__U61 a__U52 = a__U62 a__U52 = a__U63 a__U52 = a__U64 a__U52 = a__plus a__U61 = a__U62 a__U61 = a__U63 a__U61 = a__U64 a__U61 = a__plus a__U62 = a__U63 a__U62 = a__U64 a__U62 = a__plus a__U63 = a__U64 a__U63 = a__plus a__U64 = a__plus ---------------------------------------- (17) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (18) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0) -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0) -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0) -> c72 The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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 Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) [1] a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) [1] a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) [1] a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) [1] a__U15(tt, V2) -> a__U16(a__isNat(V2)) [1] a__U16(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) [1] a__U22(tt, V1) -> a__U23(a__isNat(V1)) [1] a__U23(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt) -> tt [1] a__U51(tt, N) -> a__U52(a__isNatKind(N), N) [1] a__U52(tt, N) -> mark(N) [1] a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) [1] a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) [1] a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) [1] a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) [1] a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) [1] a__plus(N, 0) -> a__U51(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) [1] mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) [1] mark(U15(X1, X2)) -> a__U15(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U16(X)) -> a__U16(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X1, X2)) -> a__U22(mark(X1), X2) [1] mark(U23(X)) -> a__U23(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X)) -> a__U41(mark(X)) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) [1] mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) [1] mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__isNatKind(X) -> isNatKind(X) [1] a__U13(X1, X2, X3) -> U13(X1, X2, X3) [1] a__U14(X1, X2, X3) -> U14(X1, X2, X3) [1] a__U15(X1, X2) -> U15(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U16(X) -> U16(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X1, X2) -> U22(X1, X2) [1] a__U23(X) -> U23(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X) -> U41(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2, X3) -> U62(X1, X2, X3) [1] a__U63(X1, X2, X3) -> U63(X1, X2, X3) [1] a__U64(X1, X2, X3) -> U64(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) [1] a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) [1] a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) [1] a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) [1] a__U15(tt, V2) -> a__U16(a__isNat(V2)) [1] a__U16(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) [1] a__U22(tt, V1) -> a__U23(a__isNat(V1)) [1] a__U23(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt) -> tt [1] a__U51(tt, N) -> a__U52(a__isNatKind(N), N) [1] a__U52(tt, N) -> mark(N) [1] a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) [1] a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) [1] a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) [1] a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) [1] a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) [1] a__plus(N, 0) -> a__U51(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) [1] mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) [1] mark(U15(X1, X2)) -> a__U15(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U16(X)) -> a__U16(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X1, X2)) -> a__U22(mark(X1), X2) [1] mark(U23(X)) -> a__U23(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X)) -> a__U41(mark(X)) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) [1] mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) [1] mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__isNatKind(X) -> isNatKind(X) [1] a__U13(X1, X2, X3) -> U13(X1, X2, X3) [1] a__U14(X1, X2, X3) -> U14(X1, X2, X3) [1] a__U15(X1, X2) -> U15(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U16(X) -> U16(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X1, X2) -> U22(X1, X2) [1] a__U23(X) -> U23(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X) -> U41(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2, X3) -> U62(X1, X2, X3) [1] a__U63(X1, X2, X3) -> U63(X1, X2, X3) [1] a__U64(X1, X2, X3) -> U64(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:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 tt :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U12 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> 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tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U61 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U62 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U63 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U64 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 Rewrite Strategy: INNERMOST ---------------------------------------- (23) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__isNatKind_1 a__isNat_1 a__U63_3 a__U32_1 a__U12_3 a__U64_3 a__U11_3 a__U15_2 a__U13_3 a__U41_1 a__U14_3 a__U62_3 a__U23_1 a__U22_2 a__U16_1 a__U51_2 a__U52_2 a__U31_2 a__U61_3 a__U21_2 a__plus_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) [1] a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) [1] a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) [1] a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) [1] a__U15(tt, V2) -> a__U16(a__isNat(V2)) [1] a__U16(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) [1] a__U22(tt, V1) -> a__U23(a__isNat(V1)) [1] a__U23(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt) -> tt [1] a__U51(tt, N) -> a__U52(a__isNatKind(N), N) [1] a__U52(tt, N) -> mark(N) [1] a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) [1] a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) [1] a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) [1] a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) [1] a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) [1] a__plus(N, 0) -> a__U51(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) [1] mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) [1] mark(U15(X1, X2)) -> a__U15(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U16(X)) -> a__U16(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X1, X2)) -> a__U22(mark(X1), X2) [1] mark(U23(X)) -> a__U23(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X)) -> a__U41(mark(X)) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) [1] mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) [1] mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__isNatKind(X) -> isNatKind(X) [1] a__U13(X1, X2, X3) -> U13(X1, X2, X3) [1] a__U14(X1, X2, X3) -> U14(X1, X2, X3) [1] a__U15(X1, X2) -> U15(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U16(X) -> U16(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X1, X2) -> U22(X1, X2) [1] a__U23(X) -> U23(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X) -> U41(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2, X3) -> U62(X1, X2, X3) [1] a__U63(X1, X2, X3) -> U63(X1, X2, X3) [1] a__U64(X1, X2, X3) -> U64(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:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 tt :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U12 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> 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tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U61 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U62 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U63 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U64 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 Rewrite Strategy: INNERMOST ---------------------------------------- (25) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 0, V2) -> a__U12(tt, 0, V2) [2] a__U11(tt, plus(V1', V2'), V2) -> a__U12(a__U31(a__isNatKind(V1'), V2'), plus(V1', V2'), V2) [2] a__U11(tt, s(V1''), V2) -> a__U12(a__U41(a__isNatKind(V1'')), s(V1''), V2) [2] a__U11(tt, V1, V2) -> a__U12(isNatKind(V1), V1, V2) [2] a__U12(tt, V1, 0) -> a__U13(tt, V1, 0) [2] a__U12(tt, V1, plus(V11, V2'')) -> a__U13(a__U31(a__isNatKind(V11), V2''), V1, plus(V11, V2'')) [2] a__U12(tt, V1, s(V12)) -> a__U13(a__U41(a__isNatKind(V12)), V1, s(V12)) [2] a__U12(tt, V1, V2) -> a__U13(isNatKind(V2), V1, V2) [2] a__U13(tt, V1, 0) -> a__U14(tt, V1, 0) [2] a__U13(tt, V1, plus(V13, V21)) -> a__U14(a__U31(a__isNatKind(V13), V21), V1, plus(V13, V21)) [2] a__U13(tt, V1, s(V14)) -> a__U14(a__U41(a__isNatKind(V14)), V1, s(V14)) [2] a__U13(tt, V1, V2) -> a__U14(isNatKind(V2), V1, V2) [2] a__U14(tt, 0, V2) -> a__U15(tt, V2) [2] a__U14(tt, plus(V15, V22), V2) -> a__U15(a__U11(a__isNatKind(V15), V15, V22), V2) [2] a__U14(tt, s(V16), V2) -> a__U15(a__U21(a__isNatKind(V16), V16), V2) [2] a__U14(tt, V1, V2) -> a__U15(isNat(V1), V2) [2] a__U15(tt, 0) -> a__U16(tt) [2] a__U15(tt, plus(V17, V23)) -> a__U16(a__U11(a__isNatKind(V17), V17, V23)) [2] a__U15(tt, s(V18)) -> a__U16(a__U21(a__isNatKind(V18), V18)) [2] a__U15(tt, V2) -> a__U16(isNat(V2)) [2] a__U16(tt) -> tt [1] a__U21(tt, 0) -> a__U22(tt, 0) [2] a__U21(tt, plus(V19, V24)) -> a__U22(a__U31(a__isNatKind(V19), V24), plus(V19, V24)) [2] a__U21(tt, s(V110)) -> a__U22(a__U41(a__isNatKind(V110)), s(V110)) [2] a__U21(tt, V1) -> a__U22(isNatKind(V1), V1) [2] a__U22(tt, 0) -> a__U23(tt) [2] a__U22(tt, plus(V111, V25)) -> a__U23(a__U11(a__isNatKind(V111), V111, V25)) [2] a__U22(tt, s(V112)) -> a__U23(a__U21(a__isNatKind(V112), V112)) [2] a__U22(tt, V1) -> a__U23(isNat(V1)) [2] a__U23(tt) -> tt [1] a__U31(tt, 0) -> a__U32(tt) [2] a__U31(tt, plus(V113, V26)) -> a__U32(a__U31(a__isNatKind(V113), V26)) [2] a__U31(tt, s(V114)) -> a__U32(a__U41(a__isNatKind(V114))) [2] a__U31(tt, V2) -> a__U32(isNatKind(V2)) [2] a__U32(tt) -> tt [1] a__U41(tt) -> tt [1] a__U51(tt, 0) -> a__U52(tt, 0) [2] a__U51(tt, plus(V115, V27)) -> a__U52(a__U31(a__isNatKind(V115), V27), plus(V115, V27)) [2] a__U51(tt, s(V116)) -> a__U52(a__U41(a__isNatKind(V116)), s(V116)) [2] a__U51(tt, N) -> a__U52(isNatKind(N), N) [2] a__U52(tt, N) -> mark(N) [1] a__U61(tt, 0, N) -> a__U62(tt, 0, N) [2] a__U61(tt, plus(V117, V28), N) -> a__U62(a__U31(a__isNatKind(V117), V28), plus(V117, V28), N) [2] a__U61(tt, s(V118), N) -> a__U62(a__U41(a__isNatKind(V118)), s(V118), N) [2] a__U61(tt, M, N) -> a__U62(isNatKind(M), M, N) [2] a__U62(tt, M, 0) -> a__U63(tt, M, 0) [2] a__U62(tt, M, plus(V119, V29)) -> a__U63(a__U11(a__isNatKind(V119), V119, V29), M, plus(V119, V29)) [2] a__U62(tt, M, s(V120)) -> a__U63(a__U21(a__isNatKind(V120), V120), M, s(V120)) [2] a__U62(tt, M, N) -> a__U63(isNat(N), M, N) [2] a__U63(tt, M, 0) -> a__U64(tt, M, 0) [2] a__U63(tt, M, plus(V121, V210)) -> a__U64(a__U31(a__isNatKind(V121), V210), M, plus(V121, V210)) [2] a__U63(tt, M, s(V122)) -> a__U64(a__U41(a__isNatKind(V122)), M, s(V122)) [2] a__U63(tt, M, N) -> a__U64(isNatKind(N), M, N) [2] a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(0, V2)) -> a__U11(tt, 0, V2) [2] a__isNat(plus(plus(V123, V211), V2)) -> a__U11(a__U31(a__isNatKind(V123), V211), plus(V123, V211), V2) [2] a__isNat(plus(s(V124), V2)) -> a__U11(a__U41(a__isNatKind(V124)), s(V124), V2) [2] a__isNat(plus(V1, V2)) -> a__U11(isNatKind(V1), V1, V2) [2] a__isNat(s(0)) -> a__U21(tt, 0) [2] a__isNat(s(plus(V125, V212))) -> a__U21(a__U31(a__isNatKind(V125), V212), plus(V125, V212)) [2] a__isNat(s(s(V126))) -> a__U21(a__U41(a__isNatKind(V126)), s(V126)) [2] a__isNat(s(V1)) -> a__U21(isNatKind(V1), V1) [2] a__isNatKind(0) -> tt [1] a__isNatKind(plus(0, V2)) -> a__U31(tt, V2) [2] a__isNatKind(plus(plus(V127, V213), V2)) -> a__U31(a__U31(a__isNatKind(V127), V213), V2) [2] a__isNatKind(plus(s(V128), V2)) -> a__U31(a__U41(a__isNatKind(V128)), V2) [2] a__isNatKind(plus(V1, V2)) -> a__U31(isNatKind(V1), V2) [2] a__isNatKind(s(0)) -> a__U41(tt) [2] a__isNatKind(s(plus(V129, V214))) -> a__U41(a__U31(a__isNatKind(V129), V214)) [2] a__isNatKind(s(s(V130))) -> a__U41(a__U41(a__isNatKind(V130))) [2] a__isNatKind(s(V1)) -> a__U41(isNatKind(V1)) [2] a__plus(0, 0) -> a__U51(tt, 0) [2] a__plus(plus(V131, V215), 0) -> a__U51(a__U11(a__isNatKind(V131), V131, V215), plus(V131, V215)) [2] a__plus(s(V132), 0) -> a__U51(a__U21(a__isNatKind(V132), V132), s(V132)) [2] a__plus(N, 0) -> a__U51(isNat(N), N) [2] a__plus(N, s(0)) -> a__U61(tt, 0, N) [2] a__plus(N, s(plus(V133, V216))) -> a__U61(a__U11(a__isNatKind(V133), V133, V216), plus(V133, V216), N) [2] a__plus(N, s(s(V134))) -> a__U61(a__U21(a__isNatKind(V134), V134), s(V134), N) [2] a__plus(N, s(M)) -> a__U61(isNat(M), M, N) [2] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) [1] mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) [1] mark(U15(X1, X2)) -> a__U15(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U16(X)) -> a__U16(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X1, X2)) -> a__U22(mark(X1), X2) [1] mark(U23(X)) -> a__U23(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X)) -> a__U41(mark(X)) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) [1] mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) [1] mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__isNatKind(X) -> isNatKind(X) [1] a__U13(X1, X2, X3) -> U13(X1, X2, X3) [1] a__U14(X1, X2, X3) -> U14(X1, X2, X3) [1] a__U15(X1, X2) -> U15(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U16(X) -> U16(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X1, X2) -> U22(X1, X2) [1] a__U23(X) -> U23(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X) -> U41(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2, X3) -> U62(X1, X2, X3) [1] a__U63(X1, X2, X3) -> U63(X1, X2, X3) [1] a__U64(X1, X2, X3) -> U64(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:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 tt :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U12 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 mark :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U61 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U62 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U63 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U64 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 s :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__plus :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 0 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 plus :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U11 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U12 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U61 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U62 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U63 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U64 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 Rewrite Strategy: INNERMOST ---------------------------------------- (27) 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 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U41(a__isNatKind(V1'')), 1 + V1'', V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U31(a__isNatKind(V1'), V2'), 1 + V1' + V2', V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, 0, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z', z'') -{ 2 }-> a__U13(a__U41(a__isNatKind(V12)), V1, 1 + V12) :|: V1 >= 0, z = 1, z'' = 1 + V12, V12 >= 0, z' = V1 a__U12(z, z', z'') -{ 2 }-> a__U13(a__U31(a__isNatKind(V11), V2''), V1, 1 + V11 + V2'') :|: V1 >= 0, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', z' = V1 a__U12(z, z', z'') -{ 2 }-> a__U13(1, V1, 0) :|: z'' = 0, V1 >= 0, z = 1, z' = V1 a__U12(z, z', z'') -{ 2 }-> a__U13(1 + V2, V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U13(z, z', z'') -{ 2 }-> a__U14(a__U41(a__isNatKind(V14)), V1, 1 + V14) :|: z'' = 1 + V14, V14 >= 0, V1 >= 0, z = 1, z' = V1 a__U13(z, z', z'') -{ 2 }-> a__U14(a__U31(a__isNatKind(V13), V21), V1, 1 + V13 + V21) :|: V21 >= 0, V1 >= 0, V13 >= 0, z = 1, z'' = 1 + V13 + V21, z' = V1 a__U13(z, z', z'') -{ 2 }-> a__U14(1, V1, 0) :|: z'' = 0, V1 >= 0, z = 1, z' = V1 a__U13(z, z', z'') -{ 2 }-> a__U14(1 + V2, V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U13(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U14(z, z', z'') -{ 2 }-> a__U15(a__U21(a__isNatKind(V16), V16), V2) :|: z = 1, z' = 1 + V16, V16 >= 0, V2 >= 0, z'' = V2 a__U14(z, z', z'') -{ 2 }-> a__U15(a__U11(a__isNatKind(V15), V15, V22), V2) :|: z' = 1 + V15 + V22, z = 1, V22 >= 0, V2 >= 0, V15 >= 0, z'' = V2 a__U14(z, z', z'') -{ 2 }-> a__U15(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U14(z, z', z'') -{ 2 }-> a__U15(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U14(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U15(z, z') -{ 2 }-> a__U16(a__U21(a__isNatKind(V18), V18)) :|: V18 >= 0, z' = 1 + V18, z = 1 a__U15(z, z') -{ 2 }-> a__U16(a__U11(a__isNatKind(V17), V17, V23)) :|: z' = 1 + V17 + V23, z = 1, V23 >= 0, V17 >= 0 a__U15(z, z') -{ 2 }-> a__U16(1) :|: z = 1, z' = 0 a__U15(z, z') -{ 2 }-> a__U16(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U15(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U16(z) -{ 1 }-> 1 :|: z = 1 a__U16(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U41(a__isNatKind(V110)), 1 + V110) :|: V110 >= 0, z = 1, z' = 1 + V110 a__U21(z, z') -{ 2 }-> a__U22(a__U31(a__isNatKind(V19), V24), 1 + V19 + V24) :|: z' = 1 + V19 + V24, V24 >= 0, z = 1, V19 >= 0 a__U21(z, z') -{ 2 }-> a__U22(1, 0) :|: z = 1, z' = 0 a__U21(z, z') -{ 2 }-> a__U22(1 + V1, V1) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z, z') -{ 2 }-> a__U23(a__U21(a__isNatKind(V112), V112)) :|: z = 1, V112 >= 0, z' = 1 + V112 a__U22(z, z') -{ 2 }-> a__U23(a__U11(a__isNatKind(V111), V111, V25)) :|: V25 >= 0, z' = 1 + V111 + V25, z = 1, V111 >= 0 a__U22(z, z') -{ 2 }-> a__U23(1) :|: z = 1, z' = 0 a__U22(z, z') -{ 2 }-> a__U23(1 + V1) :|: V1 >= 0, z = 1, z' = V1 a__U22(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U23(z) -{ 1 }-> 1 :|: z = 1 a__U23(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 2 }-> a__U32(a__U41(a__isNatKind(V114))) :|: V114 >= 0, z = 1, z' = 1 + V114 a__U31(z, z') -{ 2 }-> a__U32(a__U31(a__isNatKind(V113), V26)) :|: z' = 1 + V113 + V26, z = 1, V113 >= 0, V26 >= 0 a__U31(z, z') -{ 2 }-> a__U32(1) :|: z = 1, z' = 0 a__U31(z, z') -{ 2 }-> a__U32(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z) -{ 1 }-> 1 :|: z = 1 a__U41(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z') -{ 2 }-> a__U52(a__U41(a__isNatKind(V116)), 1 + V116) :|: z = 1, V116 >= 0, z' = 1 + V116 a__U51(z, z') -{ 2 }-> a__U52(a__U31(a__isNatKind(V115), V27), 1 + V115 + V27) :|: z' = 1 + V115 + V27, z = 1, V115 >= 0, V27 >= 0 a__U51(z, z') -{ 2 }-> a__U52(1, 0) :|: z = 1, z' = 0 a__U51(z, z') -{ 2 }-> a__U52(1 + N, N) :|: z = 1, z' = N, N >= 0 a__U51(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U52(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U41(a__isNatKind(V118)), 1 + V118, N) :|: V118 >= 0, z' = 1 + V118, z = 1, z'' = N, N >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U31(a__isNatKind(V117), V28), 1 + V117 + V28, N) :|: z' = 1 + V117 + V28, V28 >= 0, z = 1, V117 >= 0, z'' = N, N >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1, 0, N) :|: z = 1, z'' = N, z' = 0, N >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1 + M, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U62(z, z', z'') -{ 2 }-> a__U63(a__U21(a__isNatKind(V120), V120), M, 1 + V120) :|: V120 >= 0, z' = M, z = 1, z'' = 1 + V120, M >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(a__U11(a__isNatKind(V119), V119, V29), M, 1 + V119 + V29) :|: z' = M, z = 1, V29 >= 0, z'' = 1 + V119 + V29, V119 >= 0, M >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U62(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U63(z, z', z'') -{ 2 }-> a__U64(a__U41(a__isNatKind(V122)), M, 1 + V122) :|: z' = M, z = 1, V122 >= 0, z'' = 1 + V122, M >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(a__U31(a__isNatKind(V121), V210), M, 1 + V121 + V210) :|: z' = M, V121 >= 0, z = 1, V210 >= 0, z'' = 1 + V121 + V210, M >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U63(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U64(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U64(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__U41(a__isNatKind(V126)), 1 + V126) :|: z = 1 + (1 + V126), V126 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U31(a__isNatKind(V125), V212), 1 + V125 + V212) :|: V125 >= 0, z = 1 + (1 + V125 + V212), V212 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U41(a__isNatKind(V124)), 1 + V124, V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2 a__isNat(z) -{ 2 }-> a__U11(a__U31(a__isNatKind(V123), V211), 1 + V123 + V211, V2) :|: z = 1 + (1 + V123 + V211) + V2, V2 >= 0, V211 >= 0, V123 >= 0 a__isNat(z) -{ 2 }-> a__U11(1, 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 2 }-> a__U41(a__U41(a__isNatKind(V130))) :|: V130 >= 0, z = 1 + (1 + V130) a__isNatKind(z) -{ 2 }-> a__U41(a__U31(a__isNatKind(V129), V214)) :|: V214 >= 0, V129 >= 0, z = 1 + (1 + V129 + V214) a__isNatKind(z) -{ 2 }-> a__U41(1) :|: z = 1 + 0 a__isNatKind(z) -{ 2 }-> a__U41(1 + V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 2 }-> a__U31(a__U41(a__isNatKind(V128)), V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2 a__isNatKind(z) -{ 2 }-> a__U31(a__U31(a__isNatKind(V127), V213), V2) :|: V213 >= 0, z = 1 + (1 + V127 + V213) + V2, V127 >= 0, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__U31(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatKind(z) -{ 2 }-> a__U31(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U61(a__U21(a__isNatKind(V134), V134), 1 + V134, N) :|: z = N, z' = 1 + (1 + V134), V134 >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U61(a__U11(a__isNatKind(V133), V133, V216), 1 + V133 + V216, N) :|: z' = 1 + (1 + V133 + V216), z = N, V216 >= 0, N >= 0, V133 >= 0 a__plus(z, z') -{ 2 }-> a__U61(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U61(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U21(a__isNatKind(V132), V132), 1 + V132) :|: z = 1 + V132, V132 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(a__U11(a__isNatKind(V131), V131, V215), 1 + V131 + V215) :|: V131 >= 0, V215 >= 0, z = 1 + V131 + V215, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(1 + N, N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U64(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U63(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U23(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U22(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U16(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U15(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U14(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U13(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (29) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__U16(z) -{ 1 }-> 1 :|: z = 1 a__U16(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U23(z) -{ 1 }-> 1 :|: z = 1 a__U23(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U41(z) -{ 1 }-> 1 :|: z = 1 a__U41(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U41(a__isNatKind(V1'')), 1 + V1'', V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U31(a__isNatKind(V1'), V2'), 1 + V1' + V2', V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, 0, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z', z'') -{ 2 }-> a__U13(a__U41(a__isNatKind(V12)), V1, 1 + V12) :|: V1 >= 0, z = 1, z'' = 1 + V12, V12 >= 0, z' = V1 a__U12(z, z', z'') -{ 2 }-> a__U13(a__U31(a__isNatKind(V11), V2''), V1, 1 + V11 + V2'') :|: V1 >= 0, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', z' = V1 a__U12(z, z', z'') -{ 2 }-> a__U13(1, V1, 0) :|: z'' = 0, V1 >= 0, z = 1, z' = V1 a__U12(z, z', z'') -{ 2 }-> a__U13(1 + V2, V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U13(z, z', z'') -{ 2 }-> a__U14(a__U41(a__isNatKind(V14)), V1, 1 + V14) :|: z'' = 1 + V14, V14 >= 0, V1 >= 0, z = 1, z' = V1 a__U13(z, z', z'') -{ 2 }-> a__U14(a__U31(a__isNatKind(V13), V21), V1, 1 + V13 + V21) :|: V21 >= 0, V1 >= 0, V13 >= 0, z = 1, z'' = 1 + V13 + V21, z' = V1 a__U13(z, z', z'') -{ 2 }-> a__U14(1, V1, 0) :|: z'' = 0, V1 >= 0, z = 1, z' = V1 a__U13(z, z', z'') -{ 2 }-> a__U14(1 + V2, V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U13(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U14(z, z', z'') -{ 2 }-> a__U15(a__U21(a__isNatKind(V16), V16), V2) :|: z = 1, z' = 1 + V16, V16 >= 0, V2 >= 0, z'' = V2 a__U14(z, z', z'') -{ 2 }-> a__U15(a__U11(a__isNatKind(V15), V15, V22), V2) :|: z' = 1 + V15 + V22, z = 1, V22 >= 0, V2 >= 0, V15 >= 0, z'' = V2 a__U14(z, z', z'') -{ 2 }-> a__U15(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0 a__U14(z, z', z'') -{ 2 }-> a__U15(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U14(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U15(z, z') -{ 2 }-> a__U16(a__U21(a__isNatKind(V18), V18)) :|: V18 >= 0, z' = 1 + V18, z = 1 a__U15(z, z') -{ 2 }-> a__U16(a__U11(a__isNatKind(V17), V17, V23)) :|: z' = 1 + V17 + V23, z = 1, V23 >= 0, V17 >= 0 a__U15(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U15(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U15(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U15(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U15(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U16(z) -{ 1 }-> 1 :|: z = 1 a__U16(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U41(a__isNatKind(V110)), 1 + V110) :|: V110 >= 0, z = 1, z' = 1 + V110 a__U21(z, z') -{ 2 }-> a__U22(a__U31(a__isNatKind(V19), V24), 1 + V19 + V24) :|: z' = 1 + V19 + V24, V24 >= 0, z = 1, V19 >= 0 a__U21(z, z') -{ 2 }-> a__U22(1, 0) :|: z = 1, z' = 0 a__U21(z, z') -{ 2 }-> a__U22(1 + V1, V1) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z, z') -{ 2 }-> a__U23(a__U21(a__isNatKind(V112), V112)) :|: z = 1, V112 >= 0, z' = 1 + V112 a__U22(z, z') -{ 2 }-> a__U23(a__U11(a__isNatKind(V111), V111, V25)) :|: V25 >= 0, z' = 1 + V111 + V25, z = 1, V111 >= 0 a__U22(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U22(z, z') -{ 3 }-> 1 :|: V1 >= 0, z = 1, z' = V1, 1 + V1 = 1 a__U22(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U22(z, z') -{ 3 }-> 1 + X :|: V1 >= 0, z = 1, z' = V1, X >= 0, 1 + V1 = X a__U22(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U23(z) -{ 1 }-> 1 :|: z = 1 a__U23(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 2 }-> a__U32(a__U41(a__isNatKind(V114))) :|: V114 >= 0, z = 1, z' = 1 + V114 a__U31(z, z') -{ 2 }-> a__U32(a__U31(a__isNatKind(V113), V26)) :|: z' = 1 + V113 + V26, z = 1, V113 >= 0, V26 >= 0 a__U31(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U31(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U31(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U31(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z) -{ 1 }-> 1 :|: z = 1 a__U41(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z') -{ 2 }-> a__U52(a__U41(a__isNatKind(V116)), 1 + V116) :|: z = 1, V116 >= 0, z' = 1 + V116 a__U51(z, z') -{ 2 }-> a__U52(a__U31(a__isNatKind(V115), V27), 1 + V115 + V27) :|: z' = 1 + V115 + V27, z = 1, V115 >= 0, V27 >= 0 a__U51(z, z') -{ 2 }-> a__U52(1, 0) :|: z = 1, z' = 0 a__U51(z, z') -{ 2 }-> a__U52(1 + N, N) :|: z = 1, z' = N, N >= 0 a__U51(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U52(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U41(a__isNatKind(V118)), 1 + V118, N) :|: V118 >= 0, z' = 1 + V118, z = 1, z'' = N, N >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U31(a__isNatKind(V117), V28), 1 + V117 + V28, N) :|: z' = 1 + V117 + V28, V28 >= 0, z = 1, V117 >= 0, z'' = N, N >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1, 0, N) :|: z = 1, z'' = N, z' = 0, N >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1 + M, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U62(z, z', z'') -{ 2 }-> a__U63(a__U21(a__isNatKind(V120), V120), M, 1 + V120) :|: V120 >= 0, z' = M, z = 1, z'' = 1 + V120, M >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(a__U11(a__isNatKind(V119), V119, V29), M, 1 + V119 + V29) :|: z' = M, z = 1, V29 >= 0, z'' = 1 + V119 + V29, V119 >= 0, M >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U62(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U63(z, z', z'') -{ 2 }-> a__U64(a__U41(a__isNatKind(V122)), M, 1 + V122) :|: z' = M, z = 1, V122 >= 0, z'' = 1 + V122, M >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(a__U31(a__isNatKind(V121), V210), M, 1 + V121 + V210) :|: z' = M, V121 >= 0, z = 1, V210 >= 0, z'' = 1 + V121 + V210, M >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U63(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U64(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U64(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__U41(a__isNatKind(V126)), 1 + V126) :|: z = 1 + (1 + V126), V126 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U31(a__isNatKind(V125), V212), 1 + V125 + V212) :|: V125 >= 0, z = 1 + (1 + V125 + V212), V212 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U41(a__isNatKind(V124)), 1 + V124, V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2 a__isNat(z) -{ 2 }-> a__U11(a__U31(a__isNatKind(V123), V211), 1 + V123 + V211, V2) :|: z = 1 + (1 + V123 + V211) + V2, V2 >= 0, V211 >= 0, V123 >= 0 a__isNat(z) -{ 2 }-> a__U11(1, 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 2 }-> a__U41(a__U41(a__isNatKind(V130))) :|: V130 >= 0, z = 1 + (1 + V130) a__isNatKind(z) -{ 2 }-> a__U41(a__U31(a__isNatKind(V129), V214)) :|: V214 >= 0, V129 >= 0, z = 1 + (1 + V129 + V214) a__isNatKind(z) -{ 2 }-> a__U31(a__U41(a__isNatKind(V128)), V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2 a__isNatKind(z) -{ 2 }-> a__U31(a__U31(a__isNatKind(V127), V213), V2) :|: V213 >= 0, z = 1 + (1 + V127 + V213) + V2, V127 >= 0, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__U31(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatKind(z) -{ 2 }-> a__U31(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNatKind(z) -{ 3 }-> 1 :|: z = 1 + V1, V1 >= 0, 1 + V1 = 1 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X a__isNatKind(z) -{ 3 }-> 1 + X :|: z = 1 + V1, V1 >= 0, X >= 0, 1 + V1 = X a__plus(z, z') -{ 2 }-> a__U61(a__U21(a__isNatKind(V134), V134), 1 + V134, N) :|: z = N, z' = 1 + (1 + V134), V134 >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U61(a__U11(a__isNatKind(V133), V133, V216), 1 + V133 + V216, N) :|: z' = 1 + (1 + V133 + V216), z = N, V216 >= 0, N >= 0, V133 >= 0 a__plus(z, z') -{ 2 }-> a__U61(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U61(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U21(a__isNatKind(V132), V132), 1 + V132) :|: z = 1 + V132, V132 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(a__U11(a__isNatKind(V131), V131, V215), 1 + V131 + V215) :|: V131 >= 0, V215 >= 0, z = 1 + V131 + V215, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(1 + N, N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U64(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U63(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U23(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U22(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U16(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U15(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U14(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U13(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (31) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1), z'') :|: z' - 1 >= 0, z = 1, z'' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(a__U31(a__isNatKind(V1'), V2'), 1 + V1' + V2', z'') :|: z = 1, z' = 1 + V1' + V2', z'' >= 0, V2' >= 0, V1' >= 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1, 0, z'') :|: z = 1, z'' >= 0, z' = 0 a__U11(z, z', z'') -{ 2 }-> a__U12(1 + z', z', z'') :|: z' >= 0, z = 1, z'' >= 0 a__U11(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U12(z, z', z'') -{ 2 }-> a__U13(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) :|: z' >= 0, z = 1, z'' - 1 >= 0 a__U12(z, z', z'') -{ 2 }-> a__U13(a__U31(a__isNatKind(V11), V2''), z', 1 + V11 + V2'') :|: z' >= 0, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'' a__U12(z, z', z'') -{ 2 }-> a__U13(1, z', 0) :|: z'' = 0, z' >= 0, z = 1 a__U12(z, z', z'') -{ 2 }-> a__U13(1 + z'', z', z'') :|: z' >= 0, z = 1, z'' >= 0 a__U12(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U13(z, z', z'') -{ 2 }-> a__U14(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z' >= 0, z = 1 a__U13(z, z', z'') -{ 2 }-> a__U14(a__U31(a__isNatKind(V13), V21), z', 1 + V13 + V21) :|: V21 >= 0, z' >= 0, V13 >= 0, z = 1, z'' = 1 + V13 + V21 a__U13(z, z', z'') -{ 2 }-> a__U14(1, z', 0) :|: z'' = 0, z' >= 0, z = 1 a__U13(z, z', z'') -{ 2 }-> a__U14(1 + z'', z', z'') :|: z' >= 0, z = 1, z'' >= 0 a__U13(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U14(z, z', z'') -{ 2 }-> a__U15(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 1, z' - 1 >= 0, z'' >= 0 a__U14(z, z', z'') -{ 2 }-> a__U15(a__U11(a__isNatKind(V15), V15, V22), z'') :|: z' = 1 + V15 + V22, z = 1, V22 >= 0, z'' >= 0, V15 >= 0 a__U14(z, z', z'') -{ 2 }-> a__U15(1, z'') :|: z = 1, z'' >= 0, z' = 0 a__U14(z, z', z'') -{ 2 }-> a__U15(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0 a__U14(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U15(z, z') -{ 2 }-> a__U16(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z' - 1 >= 0, z = 1 a__U15(z, z') -{ 2 }-> a__U16(a__U11(a__isNatKind(V17), V17, V23)) :|: z' = 1 + V17 + V23, z = 1, V23 >= 0, V17 >= 0 a__U15(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U15(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U15(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U15(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U15(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U16(z) -{ 1 }-> 1 :|: z = 1 a__U16(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 2 }-> a__U22(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1)) :|: z' - 1 >= 0, z = 1 a__U21(z, z') -{ 2 }-> a__U22(a__U31(a__isNatKind(V19), V24), 1 + V19 + V24) :|: z' = 1 + V19 + V24, V24 >= 0, z = 1, V19 >= 0 a__U21(z, z') -{ 2 }-> a__U22(1, 0) :|: z = 1, z' = 0 a__U21(z, z') -{ 2 }-> a__U22(1 + z', z') :|: z' >= 0, z = 1 a__U21(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U22(z, z') -{ 2 }-> a__U23(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0 a__U22(z, z') -{ 2 }-> a__U23(a__U11(a__isNatKind(V111), V111, V25)) :|: V25 >= 0, z' = 1 + V111 + V25, z = 1, V111 >= 0 a__U22(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U22(z, z') -{ 3 }-> 1 :|: z' >= 0, z = 1, 1 + z' = 1 a__U22(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U22(z, z') -{ 3 }-> 1 + X :|: z' >= 0, z = 1, X >= 0, 1 + z' = X a__U22(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U23(z) -{ 1 }-> 1 :|: z = 1 a__U23(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U41(a__isNatKind(z' - 1))) :|: z' - 1 >= 0, z = 1 a__U31(z, z') -{ 2 }-> a__U32(a__U31(a__isNatKind(V113), V26)) :|: z' = 1 + V113 + V26, z = 1, V113 >= 0, V26 >= 0 a__U31(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U31(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U31(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U31(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + z :|: z >= 0 a__U41(z) -{ 1 }-> 1 :|: z = 1 a__U41(z) -{ 1 }-> 1 + z :|: z >= 0 a__U51(z, z') -{ 2 }-> a__U52(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1)) :|: z = 1, z' - 1 >= 0 a__U51(z, z') -{ 2 }-> a__U52(a__U31(a__isNatKind(V115), V27), 1 + V115 + V27) :|: z' = 1 + V115 + V27, z = 1, V115 >= 0, V27 >= 0 a__U51(z, z') -{ 2 }-> a__U52(1, 0) :|: z = 1, z' = 0 a__U51(z, z') -{ 2 }-> a__U52(1 + z', z') :|: z = 1, z' >= 0 a__U51(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U52(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__U52(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1), z'') :|: z' - 1 >= 0, z = 1, z'' >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U31(a__isNatKind(V117), V28), 1 + V117 + V28, z'') :|: z' = 1 + V117 + V28, V28 >= 0, z = 1, V117 >= 0, z'' >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1, 0, z'') :|: z = 1, z' = 0, z'' >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1 + z', z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U61(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(a__U21(a__isNatKind(z'' - 1), z'' - 1), z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(a__U11(a__isNatKind(V119), V119, V29), z', 1 + V119 + V29) :|: z = 1, V29 >= 0, z'' = 1 + V119 + V29, V119 >= 0, z' >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U62(z, z', z'') -{ 2 }-> a__U63(1 + z'', z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U62(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(a__U31(a__isNatKind(V121), V210), z', 1 + V121 + V210) :|: V121 >= 0, z = 1, V210 >= 0, z'' = 1 + V121 + V210, z' >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U63(z, z', z'') -{ 2 }-> a__U64(1 + z'', z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U63(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U64(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U64(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U41(a__isNatKind(z - 2)), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U31(a__isNatKind(V125), V212), 1 + V125 + V212) :|: V125 >= 0, z = 1 + (1 + V125 + V212), V212 >= 0 a__isNat(z) -{ 2 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U41(a__isNatKind(V124)), 1 + V124, V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2 a__isNat(z) -{ 2 }-> a__U11(a__U31(a__isNatKind(V123), V211), 1 + V123 + V211, V2) :|: z = 1 + (1 + V123 + V211) + V2, V2 >= 0, V211 >= 0, V123 >= 0 a__isNat(z) -{ 2 }-> a__U11(1, 0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 2 }-> a__U41(a__U41(a__isNatKind(z - 2))) :|: z - 2 >= 0 a__isNatKind(z) -{ 2 }-> a__U41(a__U31(a__isNatKind(V129), V214)) :|: V214 >= 0, V129 >= 0, z = 1 + (1 + V129 + V214) a__isNatKind(z) -{ 2 }-> a__U31(a__U41(a__isNatKind(V128)), V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2 a__isNatKind(z) -{ 2 }-> a__U31(a__U31(a__isNatKind(V127), V213), V2) :|: V213 >= 0, z = 1 + (1 + V127 + V213) + V2, V127 >= 0, V2 >= 0 a__isNatKind(z) -{ 2 }-> a__U31(1, z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 2 }-> a__U31(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNatKind(z) -{ 3 }-> 1 :|: z - 1 >= 0, 1 + (z - 1) = 1 a__isNatKind(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X a__isNatKind(z) -{ 3 }-> 1 + X :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X a__isNatKind(z) -{ 1 }-> 1 + z :|: z >= 0 a__plus(z, z') -{ 2 }-> a__U61(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U61(a__U11(a__isNatKind(V133), V133, V216), 1 + V133 + V216, z) :|: z' = 1 + (1 + V133 + V216), V216 >= 0, z >= 0, V133 >= 0 a__plus(z, z') -{ 2 }-> a__U61(1, 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U61(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U21(a__isNatKind(z - 1), z - 1), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(a__U11(a__isNatKind(V131), V131, V215), 1 + V131 + V215) :|: V131 >= 0, V215 >= 0, z = 1 + V131 + V215, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U51(1 + z, z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U64(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U63(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U32(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U23(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U22(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U16(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U15(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U14(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U13(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (33) 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 ---------------------------------------- (34) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__isNatKind(V1), V1, V2) [1] a__U12(tt, V1, V2) -> a__U13(a__isNatKind(V2), V1, V2) [1] a__U13(tt, V1, V2) -> a__U14(a__isNatKind(V2), V1, V2) [1] a__U14(tt, V1, V2) -> a__U15(a__isNat(V1), V2) [1] a__U15(tt, V2) -> a__U16(a__isNat(V2)) [1] a__U16(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1) [1] a__U22(tt, V1) -> a__U23(a__isNat(V1)) [1] a__U23(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNatKind(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt) -> tt [1] a__U51(tt, N) -> a__U52(a__isNatKind(N), N) [1] a__U52(tt, N) -> mark(N) [1] a__U61(tt, M, N) -> a__U62(a__isNatKind(M), M, N) [1] a__U62(tt, M, N) -> a__U63(a__isNat(N), M, N) [1] a__U63(tt, M, N) -> a__U64(a__isNatKind(N), M, N) [1] a__U64(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatKind(0) -> tt [1] a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2) [1] a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1)) [1] a__plus(N, 0) -> a__U51(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N) [1] mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1] mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3) [1] mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3) [1] mark(U15(X1, X2)) -> a__U15(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U16(X)) -> a__U16(mark(X)) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X1, X2)) -> a__U22(mark(X1), X2) [1] mark(U23(X)) -> a__U23(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X)) -> a__U41(mark(X)) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3) [1] mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3) [1] mark(U64(X1, X2, X3)) -> a__U64(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, X3) -> U11(X1, X2, X3) [1] a__U12(X1, X2, X3) -> U12(X1, X2, X3) [1] a__isNatKind(X) -> isNatKind(X) [1] a__U13(X1, X2, X3) -> U13(X1, X2, X3) [1] a__U14(X1, X2, X3) -> U14(X1, X2, X3) [1] a__U15(X1, X2) -> U15(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__U16(X) -> U16(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X1, X2) -> U22(X1, X2) [1] a__U23(X) -> U23(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X) -> U41(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2, X3) -> U62(X1, X2, X3) [1] a__U63(X1, X2, X3) -> U63(X1, X2, X3) [1] a__U64(X1, X2, X3) -> U64(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:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 tt :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U12 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 mark :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U61 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U62 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U63 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__U64 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 s :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 a__plus :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 0 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 plus :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U11 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U12 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 isNatKind :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U13 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U14 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U15 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 isNat :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U16 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U21 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U22 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U23 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U31 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U32 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U41 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U51 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U52 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U61 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U62 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U63 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 U64 :: tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 -> tt:s:0:plus:U11:U12:isNatKind:U13:U14:U15:isNat:U16:U21:U22:U23:U31:U32:U41:U51:U52:U61:U62:U63:U64 Rewrite Strategy: INNERMOST ---------------------------------------- (35) 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 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 1 }-> a__U12(a__isNatKind(V1), V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U12(z, z', z'') -{ 1 }-> a__U13(a__isNatKind(V2), V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U13(z, z', z'') -{ 1 }-> a__U14(a__isNatKind(V2), V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U13(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U14(z, z', z'') -{ 1 }-> a__U15(a__isNat(V1), V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1 a__U14(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U15(z, z') -{ 1 }-> a__U16(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U15(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U16(z) -{ 1 }-> 1 :|: z = 1 a__U16(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 1 }-> a__U22(a__isNatKind(V1), V1) :|: V1 >= 0, z = 1, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z, z') -{ 1 }-> a__U23(a__isNat(V1)) :|: V1 >= 0, z = 1, z' = V1 a__U22(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U23(z) -{ 1 }-> 1 :|: z = 1 a__U23(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> a__U32(a__isNatKind(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z) -{ 1 }-> 1 :|: z = 1 a__U41(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z') -{ 1 }-> a__U52(a__isNatKind(N), N) :|: z = 1, z' = N, N >= 0 a__U51(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U52(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U61(z, z', z'') -{ 1 }-> a__U62(a__isNatKind(M), M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U62(z, z', z'') -{ 1 }-> a__U63(a__isNat(N), M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U62(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U63(z, z', z'') -{ 1 }-> a__U64(a__isNatKind(N), M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U63(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U64(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U64(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__isNatKind(V1), V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__isNatKind(V1), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__U41(a__isNatKind(V1)) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> a__U31(a__isNatKind(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatKind(z) -{ 1 }-> 1 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 1 }-> a__U61(a__isNat(M), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U51(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__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U64(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U63(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U23(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U22(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U16(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U15(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U14(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U13(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (37) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0) -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0) -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0) -> c72 S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U11(z0, z1, z2) -> c1 A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U12(z0, z1, z2) -> c3 A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(z0, z1, z2) -> c5 A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U14(z0, z1, z2) -> c7 A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U15(z0, z1) -> c9 A__U16(tt) -> c10 A__U16(z0) -> c11 A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U21(z0, z1) -> c13 A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U22(z0, z1) -> c15 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U31(z0, z1) -> c19 A__U32(tt) -> c20 A__U32(z0) -> c21 A__U41(tt) -> c22 A__U41(z0) -> c23 A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(z0, z1) -> c25 A__U52(tt, z0) -> c26(MARK(z0)) A__U52(z0, z1) -> c27 A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U61(z0, z1, z2) -> c29 A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U62(z0, z1, z2) -> c31 A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U63(z0, z1, z2) -> c33 A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U64(z0, z1, z2) -> c36 A__ISNAT(0) -> c37 A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c40 A__ISNATKIND(0) -> c41 A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c44 A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c47 MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c70 MARK(s(z0)) -> c71(MARK(z0)) MARK(0) -> c72 K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U15_2, A__U16_1, A__U21_2, A__U22_2, A__U23_1, A__U31_2, A__U32_1, A__U41_1, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c1, c2_2, c3, c4_2, c5, c6_2, c7, c8_2, c9, c10, c11, c12_2, c13, c14_2, c15, c16, c17, c18_2, c19, c20, c21, c22, c23, c24_2, c25, c26_1, c27, c28_2, c29, c30_2, c31, c32_2, c33, c34_2, c35_2, c36, c37, c38_2, c39_2, c40, c41, c42_2, c43_2, c44, c45_2, c46_2, c47, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c55_2, c56_2, c57_2, c58_2, c59_2, c60_2, c61_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c70, c71_1, c72 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 29 trailing nodes: A__U32(tt) -> c20 A__U61(z0, z1, z2) -> c29 A__U41(z0) -> c23 A__ISNAT(z0) -> c40 A__U41(tt) -> c22 A__U23(tt) -> c16 A__U16(z0) -> c11 A__U51(z0, z1) -> c25 A__U63(z0, z1, z2) -> c33 A__U31(z0, z1) -> c19 A__U12(z0, z1, z2) -> c3 A__U11(z0, z1, z2) -> c1 A__U64(z0, z1, z2) -> c36 MARK(tt) -> c70 A__U14(z0, z1, z2) -> c7 A__U15(z0, z1) -> c9 A__PLUS(z0, z1) -> c47 A__ISNATKIND(z0) -> c44 A__ISNATKIND(0) -> c41 A__U62(z0, z1, z2) -> c31 A__U32(z0) -> c21 A__U23(z0) -> c17 MARK(0) -> c72 A__U13(z0, z1, z2) -> c5 A__U16(tt) -> c10 A__U22(z0, z1) -> c15 A__U21(z0, z1) -> c13 A__ISNAT(0) -> c37 A__U52(z0, z1) -> c27 ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U15(tt, z0) -> c8(A__U16(a__isNat(z0)), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U22(tt, z0) -> c14(A__U23(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__U32(a__isNatKind(z0)), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__U41(a__isNatKind(z0)), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U16(z0)) -> c55(A__U16(mark(z0)), MARK(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U23(z0)) -> c58(A__U23(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0)) -> c61(A__U41(mark(z0)), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U15_2, A__U21_2, A__U22_2, A__U31_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c2_2, c4_2, c6_2, c8_2, c12_2, c14_2, c18_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c43_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c55_2, c56_2, c57_2, c58_2, c59_2, c60_2, c61_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) S tuples: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2 Compound Symbols: c_2, c2_2, c4_2, c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1 ---------------------------------------- (43) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (44) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) The (relative) TRS S consists of the following rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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 Rewrite Strategy: INNERMOST ---------------------------------------- (45) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (46) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (47) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (48) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U52(tt, z0) -> c26(MARK(z0)) [1] A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) [1] MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) [1] MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) [1] MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c54(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) [1] MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) [1] MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c71(MARK(z0)) [1] A__U15(tt, z0) -> c8(A__ISNAT(z0)) [1] A__U22(tt, z0) -> c14(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) [1] MARK(U16(z0)) -> c55(MARK(z0)) [1] MARK(U23(z0)) -> c58(MARK(z0)) [1] MARK(U32(z0)) -> c60(MARK(z0)) [1] MARK(U41(z0)) -> c61(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) [0] a__U13(z0, z1, z2) -> U13(z0, z1, z2) [0] a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) [0] a__U14(z0, z1, z2) -> U14(z0, z1, z2) [0] a__U15(tt, z0) -> a__U16(a__isNat(z0)) [0] a__U15(z0, z1) -> U15(z0, z1) [0] a__U16(tt) -> tt [0] a__U16(z0) -> U16(z0) [0] a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt, z0) -> a__U23(a__isNat(z0)) [0] a__U22(z0, z1) -> U22(z0, z1) [0] a__U23(tt) -> tt [0] a__U23(z0) -> U23(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt) -> tt [0] a__U41(z0) -> U41(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt, z0) -> mark(z0) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) [0] a__U62(z0, z1, z2) -> U62(z0, z1, z2) [0] a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) [0] a__U63(z0, z1, z2) -> U63(z0, z1, z2) [0] a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U64(z0, z1, z2) -> U64(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) [0] a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) [0] mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) [0] mark(U15(z0, z1)) -> a__U15(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U16(z0)) -> a__U16(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0, z1)) -> a__U22(mark(z0), z1) [0] mark(U23(z0)) -> a__U23(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0)) -> a__U41(mark(z0)) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) [0] mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) [0] mark(U64(z0, z1, z2)) -> a__U64(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (49) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (50) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U52(tt, z0) -> c26(MARK(z0)) [1] A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) [1] MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) [1] MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) [1] MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c54(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) [1] MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) [1] MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c71(MARK(z0)) [1] A__U15(tt, z0) -> c8(A__ISNAT(z0)) [1] A__U22(tt, z0) -> c14(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) [1] MARK(U16(z0)) -> c55(MARK(z0)) [1] MARK(U23(z0)) -> c58(MARK(z0)) [1] MARK(U32(z0)) -> c60(MARK(z0)) [1] MARK(U41(z0)) -> c61(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) [0] a__U13(z0, z1, z2) -> U13(z0, z1, z2) [0] a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) [0] a__U14(z0, z1, z2) -> U14(z0, z1, z2) [0] a__U15(tt, z0) -> a__U16(a__isNat(z0)) [0] a__U15(z0, z1) -> U15(z0, z1) [0] a__U16(tt) -> tt [0] a__U16(z0) -> U16(z0) [0] a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt, z0) -> a__U23(a__isNat(z0)) [0] a__U22(z0, z1) -> U22(z0, z1) [0] a__U23(tt) -> tt [0] a__U23(z0) -> U23(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt) -> tt [0] a__U41(z0) -> U41(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt, z0) -> mark(z0) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) [0] a__U62(z0, z1, z2) -> U62(z0, z1, z2) [0] a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) [0] a__U63(z0, z1, z2) -> U63(z0, z1, z2) [0] a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U64(z0, z1, z2) -> U64(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) [0] a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) [0] mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) [0] mark(U15(z0, z1)) -> a__U15(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U16(z0)) -> a__U16(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0, z1)) -> a__U22(mark(z0), z1) [0] mark(U23(z0)) -> a__U23(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0)) -> a__U41(mark(z0)) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) [0] mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) [0] mark(U64(z0, z1, z2)) -> a__U64(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] The TRS has the following type information: A__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c tt :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c :: c2 -> c42:c43 -> c A__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c2 a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 A__ISNATKIND :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c42:c43 c2 :: c4 -> c42:c43 -> c2 A__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c4 c4 :: c6 -> c42:c43 -> c4 A__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c6 c6 :: c8 -> c38:c39 -> c6 A__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c8 a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 A__ISNAT :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c38:c39 A__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c12 c12 :: c14 -> c42:c43 -> c12 A__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c14 A__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c24 c24 :: c26 -> c42:c43 -> c24 A__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c26 c26 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c26 MARK :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 A__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c28 c28 :: c30 -> c42:c43 -> c28 A__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c30 c30 :: c32 -> c38:c39 -> c30 A__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c32 c32 :: c34:c35 -> c42:c43 -> c32 A__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c34:c35 c34 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c34:c35 A__PLUS :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c45:c46 mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c35 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c34:c35 plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c38 :: c -> c42:c43 -> c38:c39 s :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c39 :: c12 -> c42:c43 -> c38:c39 c42 :: c18 -> c42:c43 -> c42:c43 A__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> c18 0 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c45 :: c24 -> c38:c39 -> c45:c46 c46 :: c28 -> c38:c39 -> c45:c46 U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c48 :: c -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c49 :: c2 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c50 :: c42:c43 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c51 :: c4 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c52 :: c6 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c53 :: c8 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c54 :: c38:c39 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c56 :: c12 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c57 :: c14 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c59 :: c18 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c62 :: c24 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c63 :: c26 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c64 :: c28 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c65 :: c30 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c66 :: c32 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c67 :: c34:c35 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c68 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c69 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c71 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c8 :: c38:c39 -> c8 c14 :: c38:c39 -> c14 c18 :: c42:c43 -> c18 c43 :: c42:c43 -> c42:c43 U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c55 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c58 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c60 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 c61 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 a__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 a__plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41 Rewrite Strategy: INNERMOST ---------------------------------------- (51) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__U11_3 A__U12_3 A__U13_3 A__U14_3 A__U21_2 A__U51_2 A__U52_2 A__U61_3 A__U62_3 A__U63_3 A__U64_3 A__ISNAT_1 A__ISNATKIND_1 A__PLUS_2 MARK_1 A__U15_2 A__U22_2 A__U31_2 (c) The following functions are completely defined: a__U11_3 a__U12_3 a__U13_3 a__U14_3 a__U15_2 a__U16_1 a__U21_2 a__U22_2 a__U23_1 a__U31_2 a__U32_1 a__U41_1 a__U51_2 a__U52_2 a__U61_3 a__U62_3 a__U63_3 a__U64_3 a__isNat_1 a__isNatKind_1 a__plus_2 mark_1 Due to the following rules being added: a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__U13(v0, v1, v2) -> null_a__U13 [0] a__U14(v0, v1, v2) -> null_a__U14 [0] a__U15(v0, v1) -> null_a__U15 [0] a__U16(v0) -> null_a__U16 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0, v1) -> null_a__U22 [0] a__U23(v0) -> null_a__U23 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0) -> null_a__U41 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1, v2) -> null_a__U62 [0] a__U63(v0, v1, v2) -> null_a__U63 [0] a__U64(v0, v1, v2) -> null_a__U64 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__U13, null_a__U14, null_a__U15, null_a__U16, null_a__U21, null_a__U22, null_a__U23, null_a__U31, null_a__U32, null_a__U41, null_a__U51, null_a__U52, null_a__U61, null_a__U62, null_a__U63, null_a__U64, null_a__isNat, null_a__isNatKind, null_a__plus, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8, const9, const10, const11, const12, const13, const14, const15, const16, const17 ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U52(tt, z0) -> c26(MARK(z0)) [1] A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) [1] MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) [1] MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) [1] MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c54(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) [1] MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) [1] MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c71(MARK(z0)) [1] A__U15(tt, z0) -> c8(A__ISNAT(z0)) [1] A__U22(tt, z0) -> c14(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) [1] MARK(U16(z0)) -> c55(MARK(z0)) [1] MARK(U23(z0)) -> c58(MARK(z0)) [1] MARK(U32(z0)) -> c60(MARK(z0)) [1] MARK(U41(z0)) -> c61(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) [0] a__U13(z0, z1, z2) -> U13(z0, z1, z2) [0] a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) [0] a__U14(z0, z1, z2) -> U14(z0, z1, z2) [0] a__U15(tt, z0) -> a__U16(a__isNat(z0)) [0] a__U15(z0, z1) -> U15(z0, z1) [0] a__U16(tt) -> tt [0] a__U16(z0) -> U16(z0) [0] a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt, z0) -> a__U23(a__isNat(z0)) [0] a__U22(z0, z1) -> U22(z0, z1) [0] a__U23(tt) -> tt [0] a__U23(z0) -> U23(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt) -> tt [0] a__U41(z0) -> U41(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt, z0) -> mark(z0) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) [0] a__U62(z0, z1, z2) -> U62(z0, z1, z2) [0] a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) [0] a__U63(z0, z1, z2) -> U63(z0, z1, z2) [0] a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U64(z0, z1, z2) -> U64(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) [0] a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) [0] mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) [0] mark(U15(z0, z1)) -> a__U15(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U16(z0)) -> a__U16(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0, z1)) -> a__U22(mark(z0), z1) [0] mark(U23(z0)) -> a__U23(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0)) -> a__U41(mark(z0)) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) [0] mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) [0] mark(U64(z0, z1, z2)) -> a__U64(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__U13(v0, v1, v2) -> null_a__U13 [0] a__U14(v0, v1, v2) -> null_a__U14 [0] a__U15(v0, v1) -> null_a__U15 [0] a__U16(v0) -> null_a__U16 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0, v1) -> null_a__U22 [0] a__U23(v0) -> null_a__U23 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0) -> null_a__U41 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1, v2) -> null_a__U62 [0] a__U63(v0, v1, v2) -> null_a__U63 [0] a__U64(v0, v1, v2) -> null_a__U64 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c tt :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c :: c2 -> c42:c43 -> c A__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c2 a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNATKIND :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c42:c43 c2 :: c4 -> c42:c43 -> c2 A__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c4 c4 :: c6 -> c42:c43 -> c4 A__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c6 c6 :: c8 -> c38:c39 -> c6 A__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c8 a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNAT :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c38:c39 A__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c12 c12 :: c14 -> c42:c43 -> c12 A__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c14 A__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c24 c24 :: c26 -> c42:c43 -> c24 A__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c26 c26 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c26 MARK :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 A__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c28 c28 :: c30 -> c42:c43 -> c28 A__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c30 c30 :: c32 -> c38:c39 -> c30 A__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c32 c32 :: c34:c35 -> c42:c43 -> c32 A__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c34:c35 c34 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c34:c35 A__PLUS :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c45:c46 mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c35 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c34:c35 plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c38 :: c -> c42:c43 -> c38:c39 s :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c39 :: c12 -> c42:c43 -> c38:c39 c42 :: c18 -> c42:c43 -> c42:c43 A__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c18 0 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c45 :: c24 -> c38:c39 -> c45:c46 c46 :: c28 -> c38:c39 -> c45:c46 U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c48 :: c -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c49 :: c2 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c50 :: c42:c43 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c51 :: c4 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c52 :: c6 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c53 :: c8 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c54 :: c38:c39 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c56 :: c12 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c57 :: c14 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c59 :: c18 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c62 :: c24 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c63 :: c26 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c64 :: c28 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c65 :: c30 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c66 :: c32 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c67 :: c34:c35 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c68 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c69 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c71 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c8 :: c38:c39 -> c8 c14 :: c38:c39 -> c14 c18 :: c42:c43 -> c18 c43 :: c42:c43 -> c42:c43 U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c55 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c58 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c60 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c61 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 a__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark const :: c const1 :: c2 const2 :: c42:c43 const3 :: c4 const4 :: c6 const5 :: c8 const6 :: c38:c39 const7 :: c12 const8 :: c14 const9 :: c24 const10 :: c26 const11 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 const12 :: c28 const13 :: c30 const14 :: c32 const15 :: c34:c35 const16 :: c45:c46 const17 :: c18 Rewrite Strategy: INNERMOST ---------------------------------------- (53) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (54) 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, z1) -> c(A__U12(tt, 0, z1), A__ISNATKIND(0)) [1] A__U11(tt, plus(z0', z1'), z1) -> c(A__U12(a__U31(a__isNatKind(z0'), z1'), plus(z0', z1'), z1), A__ISNATKIND(plus(z0', z1'))) [1] A__U11(tt, s(z0''), z1) -> c(A__U12(a__U41(a__isNatKind(z0'')), s(z0''), z1), A__ISNATKIND(s(z0''))) [1] A__U11(tt, z0, z1) -> c(A__U12(isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U11(tt, z0, z1) -> c(A__U12(null_a__isNatKind, z0, z1), A__ISNATKIND(z0)) [1] A__U12(tt, z0, 0) -> c2(A__U13(tt, z0, 0), A__ISNATKIND(0)) [1] A__U12(tt, z0, plus(z01, z1'')) -> c2(A__U13(a__U31(a__isNatKind(z01), z1''), z0, plus(z01, z1'')), A__ISNATKIND(plus(z01, z1''))) [1] A__U12(tt, z0, s(z02)) -> c2(A__U13(a__U41(a__isNatKind(z02)), z0, s(z02)), A__ISNATKIND(s(z02))) [1] A__U12(tt, z0, z1) -> c2(A__U13(isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U12(tt, z0, z1) -> c2(A__U13(null_a__isNatKind, z0, z1), A__ISNATKIND(z1)) [1] A__U13(tt, z0, 0) -> c4(A__U14(tt, z0, 0), A__ISNATKIND(0)) [1] A__U13(tt, z0, plus(z03, z11)) -> c4(A__U14(a__U31(a__isNatKind(z03), z11), z0, plus(z03, z11)), A__ISNATKIND(plus(z03, z11))) [1] A__U13(tt, z0, s(z04)) -> c4(A__U14(a__U41(a__isNatKind(z04)), z0, s(z04)), A__ISNATKIND(s(z04))) [1] A__U13(tt, z0, z1) -> c4(A__U14(isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U13(tt, z0, z1) -> c4(A__U14(null_a__isNatKind, z0, z1), A__ISNATKIND(z1)) [1] A__U14(tt, 0, z1) -> c6(A__U15(tt, z1), A__ISNAT(0)) [1] A__U14(tt, plus(z05, z12), z1) -> c6(A__U15(a__U11(a__isNatKind(z05), z05, z12), z1), A__ISNAT(plus(z05, z12))) [1] A__U14(tt, s(z06), z1) -> c6(A__U15(a__U21(a__isNatKind(z06), z06), z1), A__ISNAT(s(z06))) [1] A__U14(tt, z0, z1) -> c6(A__U15(isNat(z0), z1), A__ISNAT(z0)) [1] A__U14(tt, z0, z1) -> c6(A__U15(null_a__isNat, z1), A__ISNAT(z0)) [1] A__U21(tt, 0) -> c12(A__U22(tt, 0), A__ISNATKIND(0)) [1] A__U21(tt, plus(z07, z13)) -> c12(A__U22(a__U31(a__isNatKind(z07), z13), plus(z07, z13)), A__ISNATKIND(plus(z07, z13))) [1] A__U21(tt, s(z08)) -> c12(A__U22(a__U41(a__isNatKind(z08)), s(z08)), A__ISNATKIND(s(z08))) [1] A__U21(tt, z0) -> c12(A__U22(isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U21(tt, z0) -> c12(A__U22(null_a__isNatKind, z0), A__ISNATKIND(z0)) [1] A__U51(tt, 0) -> c24(A__U52(tt, 0), A__ISNATKIND(0)) [1] A__U51(tt, plus(z09, z14)) -> c24(A__U52(a__U31(a__isNatKind(z09), z14), plus(z09, z14)), A__ISNATKIND(plus(z09, z14))) [1] A__U51(tt, s(z010)) -> c24(A__U52(a__U41(a__isNatKind(z010)), s(z010)), A__ISNATKIND(s(z010))) [1] A__U51(tt, z0) -> c24(A__U52(isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U51(tt, z0) -> c24(A__U52(null_a__isNatKind, z0), A__ISNATKIND(z0)) [1] A__U52(tt, z0) -> c26(MARK(z0)) [1] A__U61(tt, 0, z1) -> c28(A__U62(tt, 0, z1), A__ISNATKIND(0)) [1] A__U61(tt, plus(z011, z15), z1) -> c28(A__U62(a__U31(a__isNatKind(z011), z15), plus(z011, z15), z1), A__ISNATKIND(plus(z011, z15))) [1] A__U61(tt, s(z012), z1) -> c28(A__U62(a__U41(a__isNatKind(z012)), s(z012), z1), A__ISNATKIND(s(z012))) [1] A__U61(tt, z0, z1) -> c28(A__U62(isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U61(tt, z0, z1) -> c28(A__U62(null_a__isNatKind, z0, z1), A__ISNATKIND(z0)) [1] A__U62(tt, z0, 0) -> c30(A__U63(tt, z0, 0), A__ISNAT(0)) [1] A__U62(tt, z0, plus(z013, z16)) -> c30(A__U63(a__U11(a__isNatKind(z013), z013, z16), z0, plus(z013, z16)), A__ISNAT(plus(z013, z16))) [1] A__U62(tt, z0, s(z014)) -> c30(A__U63(a__U21(a__isNatKind(z014), z014), z0, s(z014)), A__ISNAT(s(z014))) [1] A__U62(tt, z0, z1) -> c30(A__U63(isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U62(tt, z0, z1) -> c30(A__U63(null_a__isNat, z0, z1), A__ISNAT(z1)) [1] A__U63(tt, z0, 0) -> c32(A__U64(tt, z0, 0), A__ISNATKIND(0)) [1] A__U63(tt, z0, plus(z015, z17)) -> c32(A__U64(a__U31(a__isNatKind(z015), z17), z0, plus(z015, z17)), A__ISNATKIND(plus(z015, z17))) [1] A__U63(tt, z0, s(z016)) -> c32(A__U64(a__U41(a__isNatKind(z016)), z0, s(z016)), A__ISNATKIND(s(z016))) [1] A__U63(tt, z0, z1) -> c32(A__U64(isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U63(tt, z0, z1) -> c32(A__U64(null_a__isNatKind, z0, z1), A__ISNATKIND(z1)) [1] A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__ISNAT(plus(0, z1)) -> c38(A__U11(tt, 0, z1), A__ISNATKIND(0)) [1] A__ISNAT(plus(plus(z01161, z1788), z1)) -> c38(A__U11(a__U31(a__isNatKind(z01161), z1788), plus(z01161, z1788), z1), A__ISNATKIND(plus(z01161, z1788))) [1] A__ISNAT(plus(s(z01162), z1)) -> c38(A__U11(a__U41(a__isNatKind(z01162)), s(z01162), z1), A__ISNATKIND(s(z01162))) [1] A__ISNAT(plus(z0, z1)) -> c38(A__U11(isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__ISNAT(plus(z0, z1)) -> c38(A__U11(null_a__isNatKind, z0, z1), A__ISNATKIND(z0)) [1] A__ISNAT(s(0)) -> c39(A__U21(tt, 0), A__ISNATKIND(0)) [1] A__ISNAT(s(plus(z01163, z1789))) -> c39(A__U21(a__U31(a__isNatKind(z01163), z1789), plus(z01163, z1789)), A__ISNATKIND(plus(z01163, z1789))) [1] A__ISNAT(s(s(z01164))) -> c39(A__U21(a__U41(a__isNatKind(z01164)), s(z01164)), A__ISNATKIND(s(z01164))) [1] A__ISNAT(s(z0)) -> c39(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c39(A__U21(null_a__isNatKind, z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(0, z1)) -> c42(A__U31(tt, z1), A__ISNATKIND(0)) [1] A__ISNATKIND(plus(plus(z01165, z1790), z1)) -> c42(A__U31(a__U31(a__isNatKind(z01165), z1790), z1), A__ISNATKIND(plus(z01165, z1790))) [1] A__ISNATKIND(plus(s(z01166), z1)) -> c42(A__U31(a__U41(a__isNatKind(z01166)), z1), A__ISNATKIND(s(z01166))) [1] A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(isNatKind(z0), z1), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(null_a__isNatKind, z1), A__ISNATKIND(z0)) [1] A__PLUS(0, 0) -> c45(A__U51(tt, 0), A__ISNAT(0)) [1] A__PLUS(plus(z01167, z1791), 0) -> c45(A__U51(a__U11(a__isNatKind(z01167), z01167, z1791), plus(z01167, z1791)), A__ISNAT(plus(z01167, z1791))) [1] A__PLUS(s(z01168), 0) -> c45(A__U51(a__U21(a__isNatKind(z01168), z01168), s(z01168)), A__ISNAT(s(z01168))) [1] A__PLUS(z0, 0) -> c45(A__U51(isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c45(A__U51(null_a__isNat, z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(0)) -> c46(A__U61(tt, 0, z0), A__ISNAT(0)) [1] A__PLUS(z0, s(plus(z01169, z1792))) -> c46(A__U61(a__U11(a__isNatKind(z01169), z01169, z1792), plus(z01169, z1792), z0), A__ISNAT(plus(z01169, z1792))) [1] A__PLUS(z0, s(s(z01170))) -> c46(A__U61(a__U21(a__isNatKind(z01170), z01170), s(z01170), z0), A__ISNAT(s(z01170))) [1] A__PLUS(z0, s(z1)) -> c46(A__U61(isNat(z1), z1, z0), A__ISNAT(z1)) [1] A__PLUS(z0, s(z1)) -> c46(A__U61(null_a__isNat, z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) [1] MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) [1] MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) [1] MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c54(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) [1] MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) [1] MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c71(MARK(z0)) [1] A__U15(tt, z0) -> c8(A__ISNAT(z0)) [1] A__U22(tt, z0) -> c14(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) [1] MARK(U16(z0)) -> c55(MARK(z0)) [1] MARK(U23(z0)) -> c58(MARK(z0)) [1] MARK(U32(z0)) -> c60(MARK(z0)) [1] MARK(U41(z0)) -> c61(MARK(z0)) [1] a__U11(tt, 0, z1) -> a__U12(tt, 0, z1) [0] a__U11(tt, plus(z02623, z11783), z1) -> a__U12(a__U31(a__isNatKind(z02623), z11783), plus(z02623, z11783), z1) [0] a__U11(tt, s(z02624), z1) -> a__U12(a__U41(a__isNatKind(z02624)), s(z02624), z1) [0] a__U11(tt, z0, z1) -> a__U12(isNatKind(z0), z0, z1) [0] a__U11(tt, z0, z1) -> a__U12(null_a__isNatKind, z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, 0) -> a__U13(tt, z0, 0) [0] a__U12(tt, z0, plus(z02625, z11784)) -> a__U13(a__U31(a__isNatKind(z02625), z11784), z0, plus(z02625, z11784)) [0] a__U12(tt, z0, s(z02626)) -> a__U13(a__U41(a__isNatKind(z02626)), z0, s(z02626)) [0] a__U12(tt, z0, z1) -> a__U13(isNatKind(z1), z0, z1) [0] a__U12(tt, z0, z1) -> a__U13(null_a__isNatKind, z0, z1) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__U13(tt, z0, 0) -> a__U14(tt, z0, 0) [0] a__U13(tt, z0, plus(z02627, z11785)) -> a__U14(a__U31(a__isNatKind(z02627), z11785), z0, plus(z02627, z11785)) [0] a__U13(tt, z0, s(z02628)) -> a__U14(a__U41(a__isNatKind(z02628)), z0, s(z02628)) [0] a__U13(tt, z0, z1) -> a__U14(isNatKind(z1), z0, z1) [0] a__U13(tt, z0, z1) -> a__U14(null_a__isNatKind, z0, z1) [0] a__U13(z0, z1, z2) -> U13(z0, z1, z2) [0] a__U14(tt, 0, z1) -> a__U15(tt, z1) [0] a__U14(tt, plus(z02629, z11786), z1) -> a__U15(a__U11(a__isNatKind(z02629), z02629, z11786), z1) [0] a__U14(tt, s(z02630), z1) -> a__U15(a__U21(a__isNatKind(z02630), z02630), z1) [0] a__U14(tt, z0, z1) -> a__U15(isNat(z0), z1) [0] a__U14(tt, z0, z1) -> a__U15(null_a__isNat, z1) [0] a__U14(z0, z1, z2) -> U14(z0, z1, z2) [0] a__U15(tt, 0) -> a__U16(tt) [0] a__U15(tt, plus(z02631, z11787)) -> a__U16(a__U11(a__isNatKind(z02631), z02631, z11787)) [0] a__U15(tt, s(z02632)) -> a__U16(a__U21(a__isNatKind(z02632), z02632)) [0] a__U15(tt, z0) -> a__U16(isNat(z0)) [0] a__U15(tt, z0) -> a__U16(null_a__isNat) [0] a__U15(z0, z1) -> U15(z0, z1) [0] a__U16(tt) -> tt [0] a__U16(z0) -> U16(z0) [0] a__U21(tt, 0) -> a__U22(tt, 0) [0] a__U21(tt, plus(z02633, z11788)) -> a__U22(a__U31(a__isNatKind(z02633), z11788), plus(z02633, z11788)) [0] a__U21(tt, s(z02634)) -> a__U22(a__U41(a__isNatKind(z02634)), s(z02634)) [0] a__U21(tt, z0) -> a__U22(isNatKind(z0), z0) [0] a__U21(tt, z0) -> a__U22(null_a__isNatKind, z0) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt, 0) -> a__U23(tt) [0] a__U22(tt, plus(z02635, z11789)) -> a__U23(a__U11(a__isNatKind(z02635), z02635, z11789)) [0] a__U22(tt, s(z02636)) -> a__U23(a__U21(a__isNatKind(z02636), z02636)) [0] a__U22(tt, z0) -> a__U23(isNat(z0)) [0] a__U22(tt, z0) -> a__U23(null_a__isNat) [0] a__U22(z0, z1) -> U22(z0, z1) [0] a__U23(tt) -> tt [0] a__U23(z0) -> U23(z0) [0] a__U31(tt, 0) -> a__U32(tt) [0] a__U31(tt, plus(z02637, z11790)) -> a__U32(a__U31(a__isNatKind(z02637), z11790)) [0] a__U31(tt, s(z02638)) -> a__U32(a__U41(a__isNatKind(z02638))) [0] a__U31(tt, z0) -> a__U32(isNatKind(z0)) [0] a__U31(tt, z0) -> a__U32(null_a__isNatKind) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt) -> tt [0] a__U41(z0) -> U41(z0) [0] a__U51(tt, 0) -> a__U52(tt, 0) [0] a__U51(tt, plus(z02639, z11791)) -> a__U52(a__U31(a__isNatKind(z02639), z11791), plus(z02639, z11791)) [0] a__U51(tt, s(z02640)) -> a__U52(a__U41(a__isNatKind(z02640)), s(z02640)) [0] a__U51(tt, z0) -> a__U52(isNatKind(z0), z0) [0] a__U51(tt, z0) -> a__U52(null_a__isNatKind, z0) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt, z0) -> mark(z0) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U61(tt, 0, z1) -> a__U62(tt, 0, z1) [0] a__U61(tt, plus(z02641, z11792), z1) -> a__U62(a__U31(a__isNatKind(z02641), z11792), plus(z02641, z11792), z1) [0] a__U61(tt, s(z02642), z1) -> a__U62(a__U41(a__isNatKind(z02642)), s(z02642), z1) [0] a__U61(tt, z0, z1) -> a__U62(isNatKind(z0), z0, z1) [0] a__U61(tt, z0, z1) -> a__U62(null_a__isNatKind, z0, z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0, 0) -> a__U63(tt, z0, 0) [0] a__U62(tt, z0, plus(z02643, z11793)) -> a__U63(a__U11(a__isNatKind(z02643), z02643, z11793), z0, plus(z02643, z11793)) [0] a__U62(tt, z0, s(z02644)) -> a__U63(a__U21(a__isNatKind(z02644), z02644), z0, s(z02644)) [0] a__U62(tt, z0, z1) -> a__U63(isNat(z1), z0, z1) [0] a__U62(tt, z0, z1) -> a__U63(null_a__isNat, z0, z1) [0] a__U62(z0, z1, z2) -> U62(z0, z1, z2) [0] a__U63(tt, z0, 0) -> a__U64(tt, z0, 0) [0] a__U63(tt, z0, plus(z02645, z11794)) -> a__U64(a__U31(a__isNatKind(z02645), z11794), z0, plus(z02645, z11794)) [0] a__U63(tt, z0, s(z02646)) -> a__U64(a__U41(a__isNatKind(z02646)), z0, s(z02646)) [0] a__U63(tt, z0, z1) -> a__U64(isNatKind(z1), z0, z1) [0] a__U63(tt, z0, z1) -> a__U64(null_a__isNatKind, z0, z1) [0] a__U63(z0, z1, z2) -> U63(z0, z1, z2) [0] a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U64(z0, z1, z2) -> U64(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(0, z1)) -> a__U11(tt, 0, z1) [0] a__isNat(plus(plus(z03219, z12185), z1)) -> a__U11(a__U31(a__isNatKind(z03219), z12185), plus(z03219, z12185), z1) [0] a__isNat(plus(s(z03220), z1)) -> a__U11(a__U41(a__isNatKind(z03220)), s(z03220), z1) [0] a__isNat(plus(z0, z1)) -> a__U11(isNatKind(z0), z0, z1) [0] a__isNat(plus(z0, z1)) -> a__U11(null_a__isNatKind, z0, z1) [0] a__isNat(s(0)) -> a__U21(tt, 0) [0] a__isNat(s(plus(z03221, z12186))) -> a__U21(a__U31(a__isNatKind(z03221), z12186), plus(z03221, z12186)) [0] a__isNat(s(s(z03222))) -> a__U21(a__U41(a__isNatKind(z03222)), s(z03222)) [0] a__isNat(s(z0)) -> a__U21(isNatKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(null_a__isNatKind, z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(0, z1)) -> a__U31(tt, z1) [0] a__isNatKind(plus(plus(z03223, z12187), z1)) -> a__U31(a__U31(a__isNatKind(z03223), z12187), z1) [0] a__isNatKind(plus(s(z03224), z1)) -> a__U31(a__U41(a__isNatKind(z03224)), z1) [0] a__isNatKind(plus(z0, z1)) -> a__U31(isNatKind(z0), z1) [0] a__isNatKind(plus(z0, z1)) -> a__U31(null_a__isNatKind, z1) [0] a__isNatKind(s(0)) -> a__U41(tt) [0] a__isNatKind(s(plus(z03225, z12188))) -> a__U41(a__U31(a__isNatKind(z03225), z12188)) [0] a__isNatKind(s(s(z03226))) -> a__U41(a__U41(a__isNatKind(z03226))) [0] a__isNatKind(s(z0)) -> a__U41(isNatKind(z0)) [0] a__isNatKind(s(z0)) -> a__U41(null_a__isNatKind) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(0, 0) -> a__U51(tt, 0) [0] a__plus(plus(z03227, z12189), 0) -> a__U51(a__U11(a__isNatKind(z03227), z03227, z12189), plus(z03227, z12189)) [0] a__plus(s(z03228), 0) -> a__U51(a__U21(a__isNatKind(z03228), z03228), s(z03228)) [0] a__plus(z0, 0) -> a__U51(isNat(z0), z0) [0] a__plus(z0, 0) -> a__U51(null_a__isNat, z0) [0] a__plus(z0, s(0)) -> a__U61(tt, 0, z0) [0] a__plus(z0, s(plus(z03229, z12190))) -> a__U61(a__U11(a__isNatKind(z03229), z03229, z12190), plus(z03229, z12190), z0) [0] a__plus(z0, s(s(z03230))) -> a__U61(a__U21(a__isNatKind(z03230), z03230), s(z03230), z0) [0] a__plus(z0, s(z1)) -> a__U61(isNat(z1), z1, z0) [0] a__plus(z0, s(z1)) -> a__U61(null_a__isNat, z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) [0] mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) [0] mark(U15(z0, z1)) -> a__U15(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U16(z0)) -> a__U16(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0, z1)) -> a__U22(mark(z0), z1) [0] mark(U23(z0)) -> a__U23(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0)) -> a__U41(mark(z0)) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) [0] mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) [0] mark(U64(z0, z1, z2)) -> a__U64(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__U13(v0, v1, v2) -> null_a__U13 [0] a__U14(v0, v1, v2) -> null_a__U14 [0] a__U15(v0, v1) -> null_a__U15 [0] a__U16(v0) -> null_a__U16 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0, v1) -> null_a__U22 [0] a__U23(v0) -> null_a__U23 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0) -> null_a__U41 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1, v2) -> null_a__U62 [0] a__U63(v0, v1, v2) -> null_a__U63 [0] a__U64(v0, v1, v2) -> null_a__U64 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c tt :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c :: c2 -> c42:c43 -> c A__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c2 a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNATKIND :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c42:c43 c2 :: c4 -> c42:c43 -> c2 A__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c4 c4 :: c6 -> c42:c43 -> c4 A__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c6 c6 :: c8 -> c38:c39 -> c6 A__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c8 a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNAT :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c38:c39 A__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c12 c12 :: c14 -> c42:c43 -> c12 A__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c14 A__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c24 c24 :: c26 -> c42:c43 -> c24 A__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c26 c26 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c26 MARK :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 A__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c28 c28 :: c30 -> c42:c43 -> c28 A__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c30 c30 :: c32 -> c38:c39 -> c30 A__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c32 c32 :: c34:c35 -> c42:c43 -> c32 A__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c34:c35 c34 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c34:c35 A__PLUS :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c45:c46 mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c35 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c34:c35 plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c38 :: c -> c42:c43 -> c38:c39 s :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c39 :: c12 -> c42:c43 -> c38:c39 c42 :: c18 -> c42:c43 -> c42:c43 A__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c18 0 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c45 :: c24 -> c38:c39 -> c45:c46 c46 :: c28 -> c38:c39 -> c45:c46 U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c48 :: c -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c49 :: c2 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c50 :: c42:c43 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c51 :: c4 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c52 :: c6 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c53 :: c8 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c54 :: c38:c39 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c56 :: c12 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c57 :: c14 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c59 :: c18 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c62 :: c24 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c63 :: c26 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c64 :: c28 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c65 :: c30 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c66 :: c32 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c67 :: c34:c35 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c68 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c69 :: c45:c46 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c71 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 c8 :: c38:c39 -> c8 c14 :: c38:c39 -> c14 c18 :: c42:c43 -> c18 c43 :: c42:c43 -> c42:c43 U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c55 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c58 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c60 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c61 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 a__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U22 :: 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tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark const :: c const1 :: c2 const2 :: c42:c43 const3 :: c4 const4 :: c6 const5 :: c8 const6 :: c38:c39 const7 :: c12 const8 :: c14 const9 :: c24 const10 :: c26 const11 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61 const12 :: c28 const13 :: c30 const14 :: c32 const15 :: c34:c35 const16 :: c45:c46 const17 :: c18 Rewrite Strategy: INNERMOST ---------------------------------------- (55) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U13 => 0 null_a__U14 => 0 null_a__U15 => 0 null_a__U16 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U23 => 0 null_a__U31 => 0 null_a__U32 => 0 null_a__U41 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U61 => 0 null_a__U62 => 0 null_a__U63 => 0 null_a__U64 => 0 null_a__isNat => 0 null_a__isNatKind => 0 null_a__plus => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 const7 => 0 const8 => 0 const9 => 0 const10 => 0 const11 => 0 const12 => 0 const13 => 0 const14 => 0 const15 => 0 const16 => 0 const17 => 0 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__U41(a__isNatKind(z01164)), 1 + z01164) + A__ISNATKIND(1 + z01164) :|: z = 1 + (1 + z01164), z01164 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__U31(a__isNatKind(z01163), z1789), 1 + z01163 + z1789) + A__ISNATKIND(1 + z01163 + z1789) :|: z = 1 + (1 + z01163 + z1789), z01163 >= 0, z1789 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U41(a__isNatKind(z01162)), 1 + z01162, z1) + A__ISNATKIND(1 + z01162) :|: z1 >= 0, z = 1 + (1 + z01162) + z1, z01162 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U31(a__isNatKind(z01161), z1788), 1 + z01161 + z1788, z1) + A__ISNATKIND(1 + z01161 + z1788) :|: z1788 >= 0, z1 >= 0, z = 1 + (1 + z01161 + z1788) + z1, z01161 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1, 0, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__U41(a__isNatKind(z01166)), z1) + A__ISNATKIND(1 + z01166) :|: z01166 >= 0, z1 >= 0, z = 1 + (1 + z01166) + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__U31(a__isNatKind(z01165), z1790), z1) + A__ISNATKIND(1 + z01165 + z1790) :|: z1790 >= 0, z1 >= 0, z = 1 + (1 + z01165 + z1790) + z1, z01165 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(1, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(1 + z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__U21(a__isNatKind(z01170), z01170), 1 + z01170, z0) + A__ISNAT(1 + z01170) :|: z' = 1 + (1 + z01170), z = z0, z0 >= 0, z01170 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__U11(a__isNatKind(z01169), z01169, z1792), 1 + z01169 + z1792, z0) + A__ISNAT(1 + z01169 + z1792) :|: z' = 1 + (1 + z01169 + z1792), z = z0, z01169 >= 0, z1792 >= 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(1, 0, z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(0, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(1 + z1, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__U21(a__isNatKind(z01168), z01168), 1 + z01168) + A__ISNAT(1 + z01168) :|: z01168 >= 0, z = 1 + z01168, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__U11(a__isNatKind(z01167), z01167, z1791), 1 + z01167 + z1791) + A__ISNAT(1 + z01167 + z1791) :|: z01167 >= 0, z = 1 + z01167 + z1791, z1791 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(1 + z0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U41(a__isNatKind(z0'')), 1 + z0'', z1) + A__ISNATKIND(1 + z0'') :|: z1 >= 0, z = 1, z' = 1 + z0'', z0'' >= 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U31(a__isNatKind(z0'), z1'), 1 + z0' + z1', z1) + A__ISNATKIND(1 + z0' + z1') :|: z1 >= 0, z = 1, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1', z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, 0, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__U41(a__isNatKind(z02)), z0, 1 + z02) + A__ISNATKIND(1 + z02) :|: z = 1, z02 >= 0, z0 >= 0, z' = z0, z'' = 1 + z02 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__U31(a__isNatKind(z01), z1''), z0, 1 + z01 + z1'') + A__ISNATKIND(1 + z01 + z1'') :|: z'' = 1 + z01 + z1'', z01 >= 0, z = 1, z0 >= 0, z' = z0, z1'' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(1, z0, 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(0, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(1 + z1, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__U41(a__isNatKind(z04)), z0, 1 + z04) + A__ISNATKIND(1 + z04) :|: z'' = 1 + z04, z04 >= 0, z = 1, z0 >= 0, z' = z0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__U31(a__isNatKind(z03), z11), z0, 1 + z03 + z11) + A__ISNATKIND(1 + z03 + z11) :|: z11 >= 0, z = 1, z'' = 1 + z03 + z11, z0 >= 0, z03 >= 0, z' = z0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(1, z0, 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(0, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(1 + z1, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__U21(a__isNatKind(z06), z06), z1) + A__ISNAT(1 + z06) :|: z1 >= 0, z = 1, z06 >= 0, z' = 1 + z06, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__U11(a__isNatKind(z05), z05, z12), z1) + A__ISNAT(1 + z05 + z12) :|: z1 >= 0, z = 1, z' = 1 + z05 + z12, z12 >= 0, z05 >= 0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(1, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U15(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__U41(a__isNatKind(z08)), 1 + z08) + A__ISNATKIND(1 + z08) :|: z08 >= 0, z' = 1 + z08, z = 1 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__U31(a__isNatKind(z07), z13), 1 + z07 + z13) + A__ISNATKIND(1 + z07 + z13) :|: z07 >= 0, z = 1, z13 >= 0, z' = 1 + z07 + z13 A__U21(z, z') -{ 1 }-> 1 + A__U22(1, 0) + A__ISNATKIND(0) :|: z = 1, z' = 0 A__U21(z, z') -{ 1 }-> 1 + A__U22(0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__U22(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U22(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__U41(a__isNatKind(z010)), 1 + z010) + A__ISNATKIND(1 + z010) :|: z = 1, z' = 1 + z010, z010 >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__U31(a__isNatKind(z09), z14), 1 + z09 + z14) + A__ISNATKIND(1 + z09 + z14) :|: z = 1, z' = 1 + z09 + z14, z09 >= 0, z14 >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(1, 0) + A__ISNATKIND(0) :|: z = 1, z' = 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U51(z, z') -{ 1 }-> 1 + A__U52(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U52(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U41(a__isNatKind(z012)), 1 + z012, z1) + A__ISNATKIND(1 + z012) :|: z1 >= 0, z = 1, z' = 1 + z012, z012 >= 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U31(a__isNatKind(z011), z15), 1 + z011 + z15, z1) + A__ISNATKIND(1 + z011 + z15) :|: z011 >= 0, z15 >= 0, z1 >= 0, z = 1, z' = 1 + z011 + z15, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1, 0, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__U21(a__isNatKind(z014), z014), z0, 1 + z014) + A__ISNAT(1 + z014) :|: z'' = 1 + z014, z = 1, z014 >= 0, z0 >= 0, z' = z0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__U11(a__isNatKind(z013), z013, z16), z0, 1 + z013 + z16) + A__ISNAT(1 + z013 + z16) :|: z = 1, z013 >= 0, z'' = 1 + z013 + z16, z0 >= 0, z16 >= 0, z' = z0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(1, z0, 0) + A__ISNAT(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(0, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(1 + z1, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__U41(a__isNatKind(z016)), z0, 1 + z016) + A__ISNATKIND(1 + z016) :|: z'' = 1 + z016, z = 1, z0 >= 0, z016 >= 0, z' = z0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__U31(a__isNatKind(z015), z17), z0, 1 + z015 + z17) + A__ISNATKIND(1 + z015 + z17) :|: z015 >= 0, z = 1, z17 >= 0, z0 >= 0, z'' = 1 + z015 + z17, z' = z0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(1, z0, 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(0, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(1 + z1, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U64(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U63(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U22(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U15(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U14(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U13(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U41(a__isNatKind(z02624)), 1 + z02624, z1) :|: z1 >= 0, z = 1, z' = 1 + z02624, z02624 >= 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U31(a__isNatKind(z02623), z11783), 1 + z02623 + z11783, z1) :|: z' = 1 + z02623 + z11783, z1 >= 0, z = 1, z'' = z1, z02623 >= 0, z11783 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(1, 0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1 + z0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__U41(a__isNatKind(z02626)), z0, 1 + z02626) :|: z = 1, z02626 >= 0, z'' = 1 + z02626, z0 >= 0, z' = z0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__U31(a__isNatKind(z02625), z11784), z0, 1 + z02625 + z11784) :|: z02625 >= 0, z = 1, z'' = 1 + z02625 + z11784, z11784 >= 0, z0 >= 0, z' = z0 a__U12(z, z', z'') -{ 0 }-> a__U13(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U12(z, z', z'') -{ 0 }-> a__U13(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> a__U13(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__U41(a__isNatKind(z02628)), z0, 1 + z02628) :|: z = 1, z02628 >= 0, z'' = 1 + z02628, z0 >= 0, z' = z0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__U31(a__isNatKind(z02627), z11785), z0, 1 + z02627 + z11785) :|: z = 1, z02627 >= 0, z0 >= 0, z11785 >= 0, z'' = 1 + z02627 + z11785, z' = z0 a__U13(z, z', z'') -{ 0 }-> a__U14(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U13(z, z', z'') -{ 0 }-> a__U14(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U13(z, z', z'') -{ 0 }-> a__U14(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U13(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U13(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U14(z, z', z'') -{ 0 }-> a__U15(a__U21(a__isNatKind(z02630), z02630), z1) :|: z1 >= 0, z = 1, z02630 >= 0, z' = 1 + z02630, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(a__U11(a__isNatKind(z02629), z02629, z11786), z1) :|: z11786 >= 0, z1 >= 0, z02629 >= 0, z = 1, z' = 1 + z02629 + z11786, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(1, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(1 + z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U14(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__U21(a__isNatKind(z02632), z02632)) :|: z = 1, z' = 1 + z02632, z02632 >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__U11(a__isNatKind(z02631), z02631, z11787)) :|: z02631 >= 0, z' = 1 + z02631 + z11787, z = 1, z11787 >= 0 a__U15(z, z') -{ 0 }-> a__U16(1) :|: z = 1, z' = 0 a__U15(z, z') -{ 0 }-> a__U16(0) :|: z = 1, z0 >= 0, z' = z0 a__U15(z, z') -{ 0 }-> a__U16(1 + z0) :|: z = 1, z0 >= 0, z' = z0 a__U15(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U15(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U16(z) -{ 0 }-> 1 :|: z = 1 a__U16(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U16(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U41(a__isNatKind(z02634)), 1 + z02634) :|: z = 1, z' = 1 + z02634, z02634 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U31(a__isNatKind(z02633), z11788), 1 + z02633 + z11788) :|: z' = 1 + z02633 + z11788, z = 1, z11788 >= 0, z02633 >= 0 a__U21(z, z') -{ 0 }-> a__U22(1, 0) :|: z = 1, z' = 0 a__U21(z, z') -{ 0 }-> a__U22(0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> a__U22(1 + z0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z, z') -{ 0 }-> a__U23(a__U21(a__isNatKind(z02636), z02636)) :|: z = 1, z02636 >= 0, z' = 1 + z02636 a__U22(z, z') -{ 0 }-> a__U23(a__U11(a__isNatKind(z02635), z02635, z11789)) :|: z' = 1 + z02635 + z11789, z02635 >= 0, z = 1, z11789 >= 0 a__U22(z, z') -{ 0 }-> a__U23(1) :|: z = 1, z' = 0 a__U22(z, z') -{ 0 }-> a__U23(0) :|: z = 1, z0 >= 0, z' = z0 a__U22(z, z') -{ 0 }-> a__U23(1 + z0) :|: z = 1, z0 >= 0, z' = z0 a__U22(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U22(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U23(z) -{ 0 }-> 1 :|: z = 1 a__U23(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U23(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U41(a__isNatKind(z02638))) :|: z = 1, z02638 >= 0, z' = 1 + z02638 a__U31(z, z') -{ 0 }-> a__U32(a__U31(a__isNatKind(z02637), z11790)) :|: z' = 1 + z02637 + z11790, z = 1, z11790 >= 0, z02637 >= 0 a__U31(z, z') -{ 0 }-> a__U32(1) :|: z = 1, z' = 0 a__U31(z, z') -{ 0 }-> a__U32(0) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> a__U32(1 + z0) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 1 :|: z = 1 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z) -{ 0 }-> 1 :|: z = 1 a__U41(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U41(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U41(a__isNatKind(z02640)), 1 + z02640) :|: z = 1, z02640 >= 0, z' = 1 + z02640 a__U51(z, z') -{ 0 }-> a__U52(a__U31(a__isNatKind(z02639), z11791), 1 + z02639 + z11791) :|: z02639 >= 0, z' = 1 + z02639 + z11791, z = 1, z11791 >= 0 a__U51(z, z') -{ 0 }-> a__U52(1, 0) :|: z = 1, z' = 0 a__U51(z, z') -{ 0 }-> a__U52(0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> a__U52(1 + z0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U51(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U52(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U41(a__isNatKind(z02642)), 1 + z02642, z1) :|: z02642 >= 0, z1 >= 0, z = 1, z' = 1 + z02642, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U31(a__isNatKind(z02641), z11792), 1 + z02641 + z11792, z1) :|: z1 >= 0, z02641 >= 0, z = 1, z' = 1 + z02641 + z11792, z11792 >= 0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(1, 0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(1 + z0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__U21(a__isNatKind(z02644), z02644), z0, 1 + z02644) :|: z = 1, z02644 >= 0, z'' = 1 + z02644, z0 >= 0, z' = z0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__U11(a__isNatKind(z02643), z02643, z11793), z0, 1 + z02643 + z11793) :|: z'' = 1 + z02643 + z11793, z = 1, z0 >= 0, z' = z0, z02643 >= 0, z11793 >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U62(z, z', z'') -{ 0 }-> a__U63(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U62(z, z', z'') -{ 0 }-> a__U63(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U62(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U62(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__U41(a__isNatKind(z02646)), z0, 1 + z02646) :|: z02646 >= 0, z = 1, z'' = 1 + z02646, z0 >= 0, z' = z0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__U31(a__isNatKind(z02645), z11794), z0, 1 + z02645 + z11794) :|: z02645 >= 0, z = 1, z0 >= 0, z'' = 1 + z02645 + z11794, z11794 >= 0, z' = z0 a__U63(z, z', z'') -{ 0 }-> a__U64(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U63(z, z', z'') -{ 0 }-> a__U64(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U63(z, z', z'') -{ 0 }-> a__U64(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U63(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U63(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U64(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U64(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U64(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U41(a__isNatKind(z03222)), 1 + z03222) :|: z03222 >= 0, z = 1 + (1 + z03222) a__isNat(z) -{ 0 }-> a__U21(a__U31(a__isNatKind(z03221), z12186), 1 + z03221 + z12186) :|: z03221 >= 0, z12186 >= 0, z = 1 + (1 + z03221 + z12186) a__isNat(z) -{ 0 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U41(a__isNatKind(z03220)), 1 + z03220, z1) :|: z1 >= 0, z03220 >= 0, z = 1 + (1 + z03220) + z1 a__isNat(z) -{ 0 }-> a__U11(a__U31(a__isNatKind(z03219), z12185), 1 + z03219 + z12185, z1) :|: z1 >= 0, z03219 >= 0, z = 1 + (1 + z03219 + z12185) + z1, z12185 >= 0 a__isNat(z) -{ 0 }-> a__U11(1, 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNat(z) -{ 0 }-> a__U11(0, z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__U41(a__U41(a__isNatKind(z03226))) :|: z03226 >= 0, z = 1 + (1 + z03226) a__isNatKind(z) -{ 0 }-> a__U41(a__U31(a__isNatKind(z03225), z12188)) :|: z12188 >= 0, z03225 >= 0, z = 1 + (1 + z03225 + z12188) a__isNatKind(z) -{ 0 }-> a__U41(1) :|: z = 1 + 0 a__isNatKind(z) -{ 0 }-> a__U41(0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__U41(1 + z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__U31(a__U41(a__isNatKind(z03224)), z1) :|: z1 >= 0, z03224 >= 0, z = 1 + (1 + z03224) + z1 a__isNatKind(z) -{ 0 }-> a__U31(a__U31(a__isNatKind(z03223), z12187), z1) :|: z = 1 + (1 + z03223 + z12187) + z1, z03223 >= 0, z1 >= 0, z12187 >= 0 a__isNatKind(z) -{ 0 }-> a__U31(1, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatKind(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> a__U31(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__U21(a__isNatKind(z03230), z03230), 1 + z03230, z0) :|: z03230 >= 0, z = z0, z' = 1 + (1 + z03230), z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__U11(a__isNatKind(z03229), z03229, z12190), 1 + z03229 + z12190, z0) :|: z = z0, z' = 1 + (1 + z03229 + z12190), z12190 >= 0, z03229 >= 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(1, 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(0, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U61(1 + z1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U51(a__U21(a__isNatKind(z03228), z03228), 1 + z03228) :|: z03228 >= 0, z = 1 + z03228, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(a__U11(a__isNatKind(z03227), z03227, z12189), 1 + z03227 + z12189) :|: z03227 >= 0, z12189 >= 0, z = 1 + z03227 + z12189, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(0, z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(1 + z0, z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U64(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U63(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U23(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U22(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U16(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U15(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U14(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U13(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (57) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__U16(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U16(z) -{ 0 }-> 1 :|: z = 1 a__U16(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U23(z) -{ 0 }-> 1 :|: z = 1 a__U23(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U23(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 :|: z = 1 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z) -{ 0 }-> 1 :|: z = 1 a__U41(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__U41(a__isNatKind(z01164)), 1 + z01164) + A__ISNATKIND(1 + z01164) :|: z = 1 + (1 + z01164), z01164 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__U31(a__isNatKind(z01163), z1789), 1 + z01163 + z1789) + A__ISNATKIND(1 + z01163 + z1789) :|: z = 1 + (1 + z01163 + z1789), z01163 >= 0, z1789 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U41(a__isNatKind(z01162)), 1 + z01162, z1) + A__ISNATKIND(1 + z01162) :|: z1 >= 0, z = 1 + (1 + z01162) + z1, z01162 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U31(a__isNatKind(z01161), z1788), 1 + z01161 + z1788, z1) + A__ISNATKIND(1 + z01161 + z1788) :|: z1788 >= 0, z1 >= 0, z = 1 + (1 + z01161 + z1788) + z1, z01161 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1, 0, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__U41(a__isNatKind(z01166)), z1) + A__ISNATKIND(1 + z01166) :|: z01166 >= 0, z1 >= 0, z = 1 + (1 + z01166) + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__U31(a__isNatKind(z01165), z1790), z1) + A__ISNATKIND(1 + z01165 + z1790) :|: z1790 >= 0, z1 >= 0, z = 1 + (1 + z01165 + z1790) + z1, z01165 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(1, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(1 + z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__U21(a__isNatKind(z01170), z01170), 1 + z01170, z0) + A__ISNAT(1 + z01170) :|: z' = 1 + (1 + z01170), z = z0, z0 >= 0, z01170 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__U11(a__isNatKind(z01169), z01169, z1792), 1 + z01169 + z1792, z0) + A__ISNAT(1 + z01169 + z1792) :|: z' = 1 + (1 + z01169 + z1792), z = z0, z01169 >= 0, z1792 >= 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(1, 0, z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(0, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(1 + z1, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__U21(a__isNatKind(z01168), z01168), 1 + z01168) + A__ISNAT(1 + z01168) :|: z01168 >= 0, z = 1 + z01168, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__U11(a__isNatKind(z01167), z01167, z1791), 1 + z01167 + z1791) + A__ISNAT(1 + z01167 + z1791) :|: z01167 >= 0, z = 1 + z01167 + z1791, z1791 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(1 + z0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U41(a__isNatKind(z0'')), 1 + z0'', z1) + A__ISNATKIND(1 + z0'') :|: z1 >= 0, z = 1, z' = 1 + z0'', z0'' >= 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U31(a__isNatKind(z0'), z1'), 1 + z0' + z1', z1) + A__ISNATKIND(1 + z0' + z1') :|: z1 >= 0, z = 1, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1', z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, 0, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__U41(a__isNatKind(z02)), z0, 1 + z02) + A__ISNATKIND(1 + z02) :|: z = 1, z02 >= 0, z0 >= 0, z' = z0, z'' = 1 + z02 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__U31(a__isNatKind(z01), z1''), z0, 1 + z01 + z1'') + A__ISNATKIND(1 + z01 + z1'') :|: z'' = 1 + z01 + z1'', z01 >= 0, z = 1, z0 >= 0, z' = z0, z1'' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(1, z0, 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(0, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(1 + z1, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__U41(a__isNatKind(z04)), z0, 1 + z04) + A__ISNATKIND(1 + z04) :|: z'' = 1 + z04, z04 >= 0, z = 1, z0 >= 0, z' = z0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__U31(a__isNatKind(z03), z11), z0, 1 + z03 + z11) + A__ISNATKIND(1 + z03 + z11) :|: z11 >= 0, z = 1, z'' = 1 + z03 + z11, z0 >= 0, z03 >= 0, z' = z0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(1, z0, 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(0, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(1 + z1, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__U21(a__isNatKind(z06), z06), z1) + A__ISNAT(1 + z06) :|: z1 >= 0, z = 1, z06 >= 0, z' = 1 + z06, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__U11(a__isNatKind(z05), z05, z12), z1) + A__ISNAT(1 + z05 + z12) :|: z1 >= 0, z = 1, z' = 1 + z05 + z12, z12 >= 0, z05 >= 0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(1, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U15(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__U41(a__isNatKind(z08)), 1 + z08) + A__ISNATKIND(1 + z08) :|: z08 >= 0, z' = 1 + z08, z = 1 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__U31(a__isNatKind(z07), z13), 1 + z07 + z13) + A__ISNATKIND(1 + z07 + z13) :|: z07 >= 0, z = 1, z13 >= 0, z' = 1 + z07 + z13 A__U21(z, z') -{ 1 }-> 1 + A__U22(1, 0) + A__ISNATKIND(0) :|: z = 1, z' = 0 A__U21(z, z') -{ 1 }-> 1 + A__U22(0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__U22(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U22(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__U41(a__isNatKind(z010)), 1 + z010) + A__ISNATKIND(1 + z010) :|: z = 1, z' = 1 + z010, z010 >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__U31(a__isNatKind(z09), z14), 1 + z09 + z14) + A__ISNATKIND(1 + z09 + z14) :|: z = 1, z' = 1 + z09 + z14, z09 >= 0, z14 >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(1, 0) + A__ISNATKIND(0) :|: z = 1, z' = 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U51(z, z') -{ 1 }-> 1 + A__U52(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U52(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U41(a__isNatKind(z012)), 1 + z012, z1) + A__ISNATKIND(1 + z012) :|: z1 >= 0, z = 1, z' = 1 + z012, z012 >= 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U31(a__isNatKind(z011), z15), 1 + z011 + z15, z1) + A__ISNATKIND(1 + z011 + z15) :|: z011 >= 0, z15 >= 0, z1 >= 0, z = 1, z' = 1 + z011 + z15, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1, 0, z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__U21(a__isNatKind(z014), z014), z0, 1 + z014) + A__ISNAT(1 + z014) :|: z'' = 1 + z014, z = 1, z014 >= 0, z0 >= 0, z' = z0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__U11(a__isNatKind(z013), z013, z16), z0, 1 + z013 + z16) + A__ISNAT(1 + z013 + z16) :|: z = 1, z013 >= 0, z'' = 1 + z013 + z16, z0 >= 0, z16 >= 0, z' = z0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(1, z0, 0) + A__ISNAT(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(0, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(1 + z1, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__U41(a__isNatKind(z016)), z0, 1 + z016) + A__ISNATKIND(1 + z016) :|: z'' = 1 + z016, z = 1, z0 >= 0, z016 >= 0, z' = z0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__U31(a__isNatKind(z015), z17), z0, 1 + z015 + z17) + A__ISNATKIND(1 + z015 + z17) :|: z015 >= 0, z = 1, z17 >= 0, z0 >= 0, z'' = 1 + z015 + z17, z' = z0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(1, z0, 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(0, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(1 + z1, z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U64(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U63(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U22(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U15(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U14(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U13(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U41(a__isNatKind(z02624)), 1 + z02624, z1) :|: z1 >= 0, z = 1, z' = 1 + z02624, z02624 >= 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U31(a__isNatKind(z02623), z11783), 1 + z02623 + z11783, z1) :|: z' = 1 + z02623 + z11783, z1 >= 0, z = 1, z'' = z1, z02623 >= 0, z11783 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(1, 0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> a__U12(1 + z0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__U41(a__isNatKind(z02626)), z0, 1 + z02626) :|: z = 1, z02626 >= 0, z'' = 1 + z02626, z0 >= 0, z' = z0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__U31(a__isNatKind(z02625), z11784), z0, 1 + z02625 + z11784) :|: z02625 >= 0, z = 1, z'' = 1 + z02625 + z11784, z11784 >= 0, z0 >= 0, z' = z0 a__U12(z, z', z'') -{ 0 }-> a__U13(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U12(z, z', z'') -{ 0 }-> a__U13(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> a__U13(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__U41(a__isNatKind(z02628)), z0, 1 + z02628) :|: z = 1, z02628 >= 0, z'' = 1 + z02628, z0 >= 0, z' = z0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__U31(a__isNatKind(z02627), z11785), z0, 1 + z02627 + z11785) :|: z = 1, z02627 >= 0, z0 >= 0, z11785 >= 0, z'' = 1 + z02627 + z11785, z' = z0 a__U13(z, z', z'') -{ 0 }-> a__U14(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U13(z, z', z'') -{ 0 }-> a__U14(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U13(z, z', z'') -{ 0 }-> a__U14(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U13(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U13(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U14(z, z', z'') -{ 0 }-> a__U15(a__U21(a__isNatKind(z02630), z02630), z1) :|: z1 >= 0, z = 1, z02630 >= 0, z' = 1 + z02630, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(a__U11(a__isNatKind(z02629), z02629, z11786), z1) :|: z11786 >= 0, z1 >= 0, z02629 >= 0, z = 1, z' = 1 + z02629 + z11786, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(1, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> a__U15(1 + z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U14(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__U21(a__isNatKind(z02632), z02632)) :|: z = 1, z' = 1 + z02632, z02632 >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__U11(a__isNatKind(z02631), z02631, z11787)) :|: z02631 >= 0, z' = 1 + z02631 + z11787, z = 1, z11787 >= 0 a__U15(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U15(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = 1 a__U15(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U15(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U15(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U15(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U15(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U15(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U15(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U15(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U16(z) -{ 0 }-> 1 :|: z = 1 a__U16(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U16(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U41(a__isNatKind(z02634)), 1 + z02634) :|: z = 1, z' = 1 + z02634, z02634 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U31(a__isNatKind(z02633), z11788), 1 + z02633 + z11788) :|: z' = 1 + z02633 + z11788, z = 1, z11788 >= 0, z02633 >= 0 a__U21(z, z') -{ 0 }-> a__U22(1, 0) :|: z = 1, z' = 0 a__U21(z, z') -{ 0 }-> a__U22(0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> a__U22(1 + z0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z, z') -{ 0 }-> a__U23(a__U21(a__isNatKind(z02636), z02636)) :|: z = 1, z02636 >= 0, z' = 1 + z02636 a__U22(z, z') -{ 0 }-> a__U23(a__U11(a__isNatKind(z02635), z02635, z11789)) :|: z' = 1 + z02635 + z11789, z02635 >= 0, z = 1, z11789 >= 0 a__U22(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U22(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = 1 a__U22(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U22(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U22(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U22(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U22(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U22(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U22(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U22(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U23(z) -{ 0 }-> 1 :|: z = 1 a__U23(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U23(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U41(a__isNatKind(z02638))) :|: z = 1, z02638 >= 0, z' = 1 + z02638 a__U31(z, z') -{ 0 }-> a__U32(a__U31(a__isNatKind(z02637), z11790)) :|: z' = 1 + z02637 + z11790, z = 1, z11790 >= 0, z02637 >= 0 a__U31(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U31(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = 1 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U31(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 1 :|: z = 1 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z) -{ 0 }-> 1 :|: z = 1 a__U41(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U41(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U41(a__isNatKind(z02640)), 1 + z02640) :|: z = 1, z02640 >= 0, z' = 1 + z02640 a__U51(z, z') -{ 0 }-> a__U52(a__U31(a__isNatKind(z02639), z11791), 1 + z02639 + z11791) :|: z02639 >= 0, z' = 1 + z02639 + z11791, z = 1, z11791 >= 0 a__U51(z, z') -{ 0 }-> a__U52(1, 0) :|: z = 1, z' = 0 a__U51(z, z') -{ 0 }-> a__U52(0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> a__U52(1 + z0, z0) :|: z = 1, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U51(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U52(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U41(a__isNatKind(z02642)), 1 + z02642, z1) :|: z02642 >= 0, z1 >= 0, z = 1, z' = 1 + z02642, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U31(a__isNatKind(z02641), z11792), 1 + z02641 + z11792, z1) :|: z1 >= 0, z02641 >= 0, z = 1, z' = 1 + z02641 + z11792, z11792 >= 0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(1, 0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(1 + z0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__U21(a__isNatKind(z02644), z02644), z0, 1 + z02644) :|: z = 1, z02644 >= 0, z'' = 1 + z02644, z0 >= 0, z' = z0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__U11(a__isNatKind(z02643), z02643, z11793), z0, 1 + z02643 + z11793) :|: z'' = 1 + z02643 + z11793, z = 1, z0 >= 0, z' = z0, z02643 >= 0, z11793 >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U62(z, z', z'') -{ 0 }-> a__U63(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U62(z, z', z'') -{ 0 }-> a__U63(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U62(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U62(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__U41(a__isNatKind(z02646)), z0, 1 + z02646) :|: z02646 >= 0, z = 1, z'' = 1 + z02646, z0 >= 0, z' = z0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__U31(a__isNatKind(z02645), z11794), z0, 1 + z02645 + z11794) :|: z02645 >= 0, z = 1, z0 >= 0, z'' = 1 + z02645 + z11794, z11794 >= 0, z' = z0 a__U63(z, z', z'') -{ 0 }-> a__U64(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0 a__U63(z, z', z'') -{ 0 }-> a__U64(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U63(z, z', z'') -{ 0 }-> a__U64(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U63(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U63(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U64(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U64(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U64(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U41(a__isNatKind(z03222)), 1 + z03222) :|: z03222 >= 0, z = 1 + (1 + z03222) a__isNat(z) -{ 0 }-> a__U21(a__U31(a__isNatKind(z03221), z12186), 1 + z03221 + z12186) :|: z03221 >= 0, z12186 >= 0, z = 1 + (1 + z03221 + z12186) a__isNat(z) -{ 0 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U41(a__isNatKind(z03220)), 1 + z03220, z1) :|: z1 >= 0, z03220 >= 0, z = 1 + (1 + z03220) + z1 a__isNat(z) -{ 0 }-> a__U11(a__U31(a__isNatKind(z03219), z12185), 1 + z03219 + z12185, z1) :|: z1 >= 0, z03219 >= 0, z = 1 + (1 + z03219 + z12185) + z1, z12185 >= 0 a__isNat(z) -{ 0 }-> a__U11(1, 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNat(z) -{ 0 }-> a__U11(0, z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__U41(a__U41(a__isNatKind(z03226))) :|: z03226 >= 0, z = 1 + (1 + z03226) a__isNatKind(z) -{ 0 }-> a__U41(a__U31(a__isNatKind(z03225), z12188)) :|: z12188 >= 0, z03225 >= 0, z = 1 + (1 + z03225 + z12188) a__isNatKind(z) -{ 0 }-> a__U31(a__U41(a__isNatKind(z03224)), z1) :|: z1 >= 0, z03224 >= 0, z = 1 + (1 + z03224) + z1 a__isNatKind(z) -{ 0 }-> a__U31(a__U31(a__isNatKind(z03223), z12187), z1) :|: z = 1 + (1 + z03223 + z12187) + z1, z03223 >= 0, z1 >= 0, z12187 >= 0 a__isNatKind(z) -{ 0 }-> a__U31(1, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatKind(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> a__U31(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0, 1 + z0 = 1 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 1 = v0 a__isNatKind(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 1 + z0 = v0 a__isNatKind(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 1 = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 1 + z0 = z0', z0' >= 0 a__isNatKind(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__U21(a__isNatKind(z03230), z03230), 1 + z03230, z0) :|: z03230 >= 0, z = z0, z' = 1 + (1 + z03230), z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__U11(a__isNatKind(z03229), z03229, z12190), 1 + z03229 + z12190, z0) :|: z = z0, z' = 1 + (1 + z03229 + z12190), z12190 >= 0, z03229 >= 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(1, 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(0, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U61(1 + z1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U51(a__U21(a__isNatKind(z03228), z03228), 1 + z03228) :|: z03228 >= 0, z = 1 + z03228, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(a__U11(a__isNatKind(z03227), z03227, z12189), 1 + z03227 + z12189) :|: z03227 >= 0, z12189 >= 0, z = 1 + z03227 + z12189, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(0, z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(1 + z0, z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U64(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U63(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U23(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U22(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U16(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U15(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U14(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U13(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (59) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__U41(a__isNatKind(z - 2)), 1 + (z - 2)) + A__ISNATKIND(1 + (z - 2)) :|: z - 2 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__U31(a__isNatKind(z01163), z1789), 1 + z01163 + z1789) + A__ISNATKIND(1 + z01163 + z1789) :|: z = 1 + (1 + z01163 + z1789), z01163 >= 0, z1789 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + (z - 1), z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U41(a__isNatKind(z01162)), 1 + z01162, z1) + A__ISNATKIND(1 + z01162) :|: z1 >= 0, z = 1 + (1 + z01162) + z1, z01162 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U31(a__isNatKind(z01161), z1788), 1 + z01161 + z1788, z1) + A__ISNATKIND(1 + z01161 + z1788) :|: z1788 >= 0, z1 >= 0, z = 1 + (1 + z01161 + z1788) + z1, z01161 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1, 0, z - 1) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__U41(a__isNatKind(z01166)), z1) + A__ISNATKIND(1 + z01166) :|: z01166 >= 0, z1 >= 0, z = 1 + (1 + z01166) + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__U31(a__isNatKind(z01165), z1790), z1) + A__ISNATKIND(1 + z01165 + z1790) :|: z1790 >= 0, z1 >= 0, z = 1 + (1 + z01165 + z1790) + z1, z01165 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(1, z - 1) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(1 + z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (z' - 2), z) + A__ISNAT(1 + (z' - 2)) :|: z >= 0, z' - 2 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__U11(a__isNatKind(z01169), z01169, z1792), 1 + z01169 + z1792, z) + A__ISNAT(1 + z01169 + z1792) :|: z' = 1 + (1 + z01169 + z1792), z01169 >= 0, z1792 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(1, 0, z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(0, z' - 1, z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(1 + (z' - 1), z' - 1, z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__U21(a__isNatKind(z - 1), z - 1), 1 + (z - 1)) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__U11(a__isNatKind(z01167), z01167, z1791), 1 + z01167 + z1791) + A__ISNAT(1 + z01167 + z1791) :|: z01167 >= 0, z = 1 + z01167 + z1791, z1791 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(0, z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(1 + z, z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1), z'') + A__ISNATKIND(1 + (z' - 1)) :|: z'' >= 0, z = 1, z' - 1 >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__U31(a__isNatKind(z0'), z1'), 1 + z0' + z1', z'') + A__ISNATKIND(1 + z0' + z1') :|: z'' >= 0, z = 1, z0' >= 0, z1' >= 0, z' = 1 + z0' + z1' A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, 0, z'') + A__ISNATKIND(0) :|: z'' >= 0, z = 1, z' = 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(0, z', z'') + A__ISNATKIND(z') :|: z'' >= 0, z = 1, z' >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1 + z', z', z'') + A__ISNATKIND(z') :|: z'' >= 0, z = 1, z' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) + A__ISNATKIND(1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__U31(a__isNatKind(z01), z1''), z', 1 + z01 + z1'') + A__ISNATKIND(1 + z01 + z1'') :|: z'' = 1 + z01 + z1'', z01 >= 0, z = 1, z' >= 0, z1'' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(1, z', 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(0, z', z'') + A__ISNATKIND(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(1 + z'', z', z'') + A__ISNATKIND(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) + A__ISNATKIND(1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__U31(a__isNatKind(z03), z11), z', 1 + z03 + z11) + A__ISNATKIND(1 + z03 + z11) :|: z11 >= 0, z = 1, z'' = 1 + z03 + z11, z' >= 0, z03 >= 0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(1, z', 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z' >= 0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(0, z', z'') + A__ISNATKIND(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(1 + z'', z', z'') + A__ISNATKIND(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z'' >= 0, z = 1, z' - 1 >= 0 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__U11(a__isNatKind(z05), z05, z12), z'') + A__ISNAT(1 + z05 + z12) :|: z'' >= 0, z = 1, z' = 1 + z05 + z12, z12 >= 0, z05 >= 0 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(1, z'') + A__ISNAT(0) :|: z'' >= 0, z = 1, z' = 0 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(0, z'') + A__ISNAT(z') :|: z'' >= 0, z = 1, z' >= 0 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(1 + z', z'') + A__ISNAT(z') :|: z'' >= 0, z = 1, z' >= 0 A__U15(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 1, z' >= 0 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1)) + A__ISNATKIND(1 + (z' - 1)) :|: z' - 1 >= 0, z = 1 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__U31(a__isNatKind(z07), z13), 1 + z07 + z13) + A__ISNATKIND(1 + z07 + z13) :|: z07 >= 0, z = 1, z13 >= 0, z' = 1 + z07 + z13 A__U21(z, z') -{ 1 }-> 1 + A__U22(1, 0) + A__ISNATKIND(0) :|: z = 1, z' = 0 A__U21(z, z') -{ 1 }-> 1 + A__U22(0, z') + A__ISNATKIND(z') :|: z = 1, z' >= 0 A__U21(z, z') -{ 1 }-> 1 + A__U22(1 + z', z') + A__ISNATKIND(z') :|: z = 1, z' >= 0 A__U22(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 1, z' >= 0 A__U31(z, z') -{ 1 }-> 1 + A__ISNATKIND(z') :|: z = 1, z' >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1)) + A__ISNATKIND(1 + (z' - 1)) :|: z = 1, z' - 1 >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__U31(a__isNatKind(z09), z14), 1 + z09 + z14) + A__ISNATKIND(1 + z09 + z14) :|: z = 1, z' = 1 + z09 + z14, z09 >= 0, z14 >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(1, 0) + A__ISNATKIND(0) :|: z = 1, z' = 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(0, z') + A__ISNATKIND(z') :|: z = 1, z' >= 0 A__U51(z, z') -{ 1 }-> 1 + A__U52(1 + z', z') + A__ISNATKIND(z') :|: z = 1, z' >= 0 A__U52(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 1, z' >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1), z'') + A__ISNATKIND(1 + (z' - 1)) :|: z'' >= 0, z = 1, z' - 1 >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U31(a__isNatKind(z011), z15), 1 + z011 + z15, z'') + A__ISNATKIND(1 + z011 + z15) :|: z011 >= 0, z15 >= 0, z'' >= 0, z = 1, z' = 1 + z011 + z15 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1, 0, z'') + A__ISNATKIND(0) :|: z'' >= 0, z = 1, z' = 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(0, z', z'') + A__ISNATKIND(z') :|: z'' >= 0, z = 1, z' >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1 + z', z', z'') + A__ISNATKIND(z') :|: z'' >= 0, z = 1, z' >= 0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__U21(a__isNatKind(z'' - 1), z'' - 1), z', 1 + (z'' - 1)) + A__ISNAT(1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__U11(a__isNatKind(z013), z013, z16), z', 1 + z013 + z16) + A__ISNAT(1 + z013 + z16) :|: z = 1, z013 >= 0, z'' = 1 + z013 + z16, z' >= 0, z16 >= 0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(1, z', 0) + A__ISNAT(0) :|: z'' = 0, z = 1, z' >= 0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(0, z', z'') + A__ISNAT(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(1 + z'', z', z'') + A__ISNAT(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) + A__ISNATKIND(1 + (z'' - 1)) :|: z = 1, z' >= 0, z'' - 1 >= 0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__U31(a__isNatKind(z015), z17), z', 1 + z015 + z17) + A__ISNATKIND(1 + z015 + z17) :|: z015 >= 0, z = 1, z17 >= 0, z' >= 0, z'' = 1 + z015 + z17 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(1, z', 0) + A__ISNATKIND(0) :|: z'' = 0, z = 1, z' >= 0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(0, z', z'') + A__ISNATKIND(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(1 + z'', z', z'') + A__ISNATKIND(z'') :|: z'' >= 0, z = 1, z' >= 0 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U64(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U63(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U22(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U15(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U14(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U13(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(a__U31(a__isNatKind(z02623), z11783), 1 + z02623 + z11783, z'') :|: z' = 1 + z02623 + z11783, z'' >= 0, z = 1, z02623 >= 0, z11783 >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0 a__U11(z, z', z'') -{ 0 }-> a__U12(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U11(z, z', z'') -{ 0 }-> a__U12(1 + z', z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U11(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__U31(a__isNatKind(z02625), z11784), z', 1 + z02625 + z11784) :|: z02625 >= 0, z = 1, z'' = 1 + z02625 + z11784, z11784 >= 0, z' >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(1 + z'', z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U12(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__U31(a__isNatKind(z02627), z11785), z', 1 + z02627 + z11785) :|: z = 1, z02627 >= 0, z' >= 0, z11785 >= 0, z'' = 1 + z02627 + z11785 a__U13(z, z', z'') -{ 0 }-> a__U14(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(1 + z'', z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U13(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U13(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U14(z, z', z'') -{ 0 }-> a__U15(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0 a__U14(z, z', z'') -{ 0 }-> a__U15(a__U11(a__isNatKind(z02629), z02629, z11786), z'') :|: z11786 >= 0, z'' >= 0, z02629 >= 0, z = 1, z' = 1 + z02629 + z11786 a__U14(z, z', z'') -{ 0 }-> a__U15(1, z'') :|: z'' >= 0, z = 1, z' = 0 a__U14(z, z', z'') -{ 0 }-> a__U15(0, z'') :|: z'' >= 0, z = 1, z' >= 0 a__U14(z, z', z'') -{ 0 }-> a__U15(1 + z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U14(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U14(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__U11(a__isNatKind(z02631), z02631, z11787)) :|: z02631 >= 0, z' = 1 + z02631 + z11787, z = 1, z11787 >= 0 a__U15(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U15(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U15(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U15(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U15(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 1 + z' = v0 a__U15(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 0 = v0 a__U15(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U15(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 1 + z' = z0', z0' >= 0 a__U15(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 0 = z0', z0' >= 0 a__U15(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U16(z) -{ 0 }-> 1 :|: z = 1 a__U16(z) -{ 0 }-> 0 :|: z >= 0 a__U16(z) -{ 0 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1)) :|: z = 1, z' - 1 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U31(a__isNatKind(z02633), z11788), 1 + z02633 + z11788) :|: z' = 1 + z02633 + z11788, z = 1, z11788 >= 0, z02633 >= 0 a__U21(z, z') -{ 0 }-> a__U22(1, 0) :|: z = 1, z' = 0 a__U21(z, z') -{ 0 }-> a__U22(0, z') :|: z = 1, z' >= 0 a__U21(z, z') -{ 0 }-> a__U22(1 + z', z') :|: z = 1, z' >= 0 a__U21(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U21(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U22(z, z') -{ 0 }-> a__U23(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0 a__U22(z, z') -{ 0 }-> a__U23(a__U11(a__isNatKind(z02635), z02635, z11789)) :|: z' = 1 + z02635 + z11789, z02635 >= 0, z = 1, z11789 >= 0 a__U22(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U22(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U22(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U22(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U22(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 1 + z' = v0 a__U22(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 0 = v0 a__U22(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U22(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 1 + z' = z0', z0' >= 0 a__U22(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 0 = z0', z0' >= 0 a__U22(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U23(z) -{ 0 }-> 1 :|: z = 1 a__U23(z) -{ 0 }-> 0 :|: z >= 0 a__U23(z) -{ 0 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U41(a__isNatKind(z' - 1))) :|: z = 1, z' - 1 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U31(a__isNatKind(z02637), z11790)) :|: z' = 1 + z02637 + z11790, z = 1, z11790 >= 0, z02637 >= 0 a__U31(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U31(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U31(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U31(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 1 + z' = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 0 = v0 a__U31(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 1 + z' = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 0 = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U32(z) -{ 0 }-> 1 :|: z = 1 a__U32(z) -{ 0 }-> 0 :|: z >= 0 a__U32(z) -{ 0 }-> 1 + z :|: z >= 0 a__U41(z) -{ 0 }-> 1 :|: z = 1 a__U41(z) -{ 0 }-> 0 :|: z >= 0 a__U41(z) -{ 0 }-> 1 + z :|: z >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1)) :|: z = 1, z' - 1 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U31(a__isNatKind(z02639), z11791), 1 + z02639 + z11791) :|: z02639 >= 0, z' = 1 + z02639 + z11791, z = 1, z11791 >= 0 a__U51(z, z') -{ 0 }-> a__U52(1, 0) :|: z = 1, z' = 0 a__U51(z, z') -{ 0 }-> a__U52(0, z') :|: z = 1, z' >= 0 a__U51(z, z') -{ 0 }-> a__U52(1 + z', z') :|: z = 1, z' >= 0 a__U51(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U51(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U52(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0 a__U52(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U52(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U41(a__isNatKind(z' - 1)), 1 + (z' - 1), z'') :|: z' - 1 >= 0, z'' >= 0, z = 1 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U31(a__isNatKind(z02641), z11792), 1 + z02641 + z11792, z'') :|: z'' >= 0, z02641 >= 0, z = 1, z' = 1 + z02641 + z11792, z11792 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(1, 0, z'') :|: z'' >= 0, z = 1, z' = 0 a__U61(z, z', z'') -{ 0 }-> a__U62(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(1 + z', z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U61(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__U21(a__isNatKind(z'' - 1), z'' - 1), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__U11(a__isNatKind(z02643), z02643, z11793), z', 1 + z02643 + z11793) :|: z'' = 1 + z02643 + z11793, z = 1, z' >= 0, z02643 >= 0, z11793 >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(1 + z'', z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U62(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U62(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__U41(a__isNatKind(z'' - 1)), z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__U31(a__isNatKind(z02645), z11794), z', 1 + z02645 + z11794) :|: z02645 >= 0, z = 1, z' >= 0, z'' = 1 + z02645 + z11794, z11794 >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(1 + z'', z', z'') :|: z'' >= 0, z = 1, z' >= 0 a__U63(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U63(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U64(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U64(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z''), mark(z')) :|: z'' >= 0, z = 1, z' >= 0 a__U64(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U41(a__isNatKind(z - 2)), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U31(a__isNatKind(z03221), z12186), 1 + z03221 + z12186) :|: z03221 >= 0, z12186 >= 0, z = 1 + (1 + z03221 + z12186) a__isNat(z) -{ 0 }-> a__U21(1, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U41(a__isNatKind(z03220)), 1 + z03220, z1) :|: z1 >= 0, z03220 >= 0, z = 1 + (1 + z03220) + z1 a__isNat(z) -{ 0 }-> a__U11(a__U31(a__isNatKind(z03219), z12185), 1 + z03219 + z12185, z1) :|: z1 >= 0, z03219 >= 0, z = 1 + (1 + z03219 + z12185) + z1, z12185 >= 0 a__isNat(z) -{ 0 }-> a__U11(1, 0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U11(0, z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: z >= 0 a__isNat(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 0 }-> a__U41(a__U41(a__isNatKind(z - 2))) :|: z - 2 >= 0 a__isNatKind(z) -{ 0 }-> a__U41(a__U31(a__isNatKind(z03225), z12188)) :|: z12188 >= 0, z03225 >= 0, z = 1 + (1 + z03225 + z12188) a__isNatKind(z) -{ 0 }-> a__U31(a__U41(a__isNatKind(z03224)), z1) :|: z1 >= 0, z03224 >= 0, z = 1 + (1 + z03224) + z1 a__isNatKind(z) -{ 0 }-> a__U31(a__U31(a__isNatKind(z03223), z12187), z1) :|: z = 1 + (1 + z03223 + z12187) + z1, z03223 >= 0, z1 >= 0, z12187 >= 0 a__isNatKind(z) -{ 0 }-> a__U31(1, z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> a__U31(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNatKind(z) -{ 0 }-> 1 :|: z - 1 >= 0, 1 + (z - 1) = 1 a__isNatKind(z) -{ 0 }-> 0 :|: z >= 0 a__isNatKind(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 1 = v0 a__isNatKind(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 1 + (z - 1) = v0 a__isNatKind(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0 a__isNatKind(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 1 = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 1 + (z - 1) = z0', z0' >= 0 a__isNatKind(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__U11(a__isNatKind(z03229), z03229, z12190), 1 + z03229 + z12190, z) :|: z' = 1 + (1 + z03229 + z12190), z12190 >= 0, z03229 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U61(1, 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U61(0, z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U61(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U51(a__U21(a__isNatKind(z - 1), z - 1), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(a__U11(a__isNatKind(z03227), z03227, z12189), 1 + z03227 + z12189) :|: z03227 >= 0, z12189 >= 0, z = 1 + z03227 + z12189, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(0, z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U51(1 + z, z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__plus(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U64(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U63(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U32(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U23(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U22(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U16(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U15(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U14(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U13(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (61) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__U13(v0, v1, v2) -> null_a__U13 [0] a__U14(v0, v1, v2) -> null_a__U14 [0] a__U15(v0, v1) -> null_a__U15 [0] a__U16(v0) -> null_a__U16 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0, v1) -> null_a__U22 [0] a__U23(v0) -> null_a__U23 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0) -> null_a__U41 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1, v2) -> null_a__U62 [0] a__U63(v0, v1, v2) -> null_a__U63 [0] a__U64(v0, v1, v2) -> null_a__U64 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1, v2) -> null_A__U11 [0] A__U12(v0, v1, v2) -> null_A__U12 [0] A__U13(v0, v1, v2) -> null_A__U13 [0] A__U14(v0, v1, v2) -> null_A__U14 [0] A__U21(v0, v1) -> null_A__U21 [0] A__U51(v0, v1) -> null_A__U51 [0] A__U52(v0, v1) -> null_A__U52 [0] A__U61(v0, v1, v2) -> null_A__U61 [0] A__U62(v0, v1, v2) -> null_A__U62 [0] A__U63(v0, v1, v2) -> null_A__U63 [0] A__U64(v0, v1, v2) -> null_A__U64 [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__ISNATKIND(v0) -> null_A__ISNATKIND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] A__U15(v0, v1) -> null_A__U15 [0] A__U22(v0, v1) -> null_A__U22 [0] A__U31(v0, v1) -> null_A__U31 [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__U13, null_a__U14, null_a__U15, null_a__U16, null_a__U21, null_a__U22, null_a__U23, null_a__U31, null_a__U32, null_a__U41, null_a__U51, null_a__U52, null_a__U61, null_a__U62, null_a__U63, null_a__U64, null_a__isNat, null_a__isNatKind, null_a__plus, null_mark, null_A__U11, null_A__U12, null_A__U13, null_A__U14, null_A__U21, null_A__U51, null_A__U52, null_A__U61, null_A__U62, null_A__U63, null_A__U64, null_A__ISNAT, null_A__ISNATKIND, null_A__PLUS, null_MARK, null_A__U15, null_A__U22, null_A__U31 ---------------------------------------- (62) 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, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__U52(tt, z0) -> c26(MARK(z0)) [1] A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) [1] A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) [1] A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) [1] MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) [1] MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) [1] MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) [1] MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) [1] MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c54(A__ISNAT(z0)) [1] MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) [1] MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) [1] MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) [1] MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c71(MARK(z0)) [1] A__U15(tt, z0) -> c8(A__ISNAT(z0)) [1] A__U22(tt, z0) -> c14(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) [1] MARK(U16(z0)) -> c55(MARK(z0)) [1] MARK(U23(z0)) -> c58(MARK(z0)) [1] MARK(U32(z0)) -> c60(MARK(z0)) [1] MARK(U41(z0)) -> c61(MARK(z0)) [1] a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) [0] a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0] a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) [0] a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0] a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) [0] a__U13(z0, z1, z2) -> U13(z0, z1, z2) [0] a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) [0] a__U14(z0, z1, z2) -> U14(z0, z1, z2) [0] a__U15(tt, z0) -> a__U16(a__isNat(z0)) [0] a__U15(z0, z1) -> U15(z0, z1) [0] a__U16(tt) -> tt [0] a__U16(z0) -> U16(z0) [0] a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt, z0) -> a__U23(a__isNat(z0)) [0] a__U22(z0, z1) -> U22(z0, z1) [0] a__U23(tt) -> tt [0] a__U23(z0) -> U23(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt) -> tt [0] a__U41(z0) -> U41(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt, z0) -> mark(z0) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) [0] a__U62(z0, z1, z2) -> U62(z0, z1, z2) [0] a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) [0] a__U63(z0, z1, z2) -> U63(z0, z1, z2) [0] a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U64(z0, z1, z2) -> U64(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) [0] a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0] mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) [0] mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) [0] mark(U15(z0, z1)) -> a__U15(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U16(z0)) -> a__U16(mark(z0)) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0, z1)) -> a__U22(mark(z0), z1) [0] mark(U23(z0)) -> a__U23(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0)) -> a__U41(mark(z0)) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) [0] mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) [0] mark(U64(z0, z1, z2)) -> a__U64(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1, v2) -> null_a__U11 [0] a__U12(v0, v1, v2) -> null_a__U12 [0] a__U13(v0, v1, v2) -> null_a__U13 [0] a__U14(v0, v1, v2) -> null_a__U14 [0] a__U15(v0, v1) -> null_a__U15 [0] a__U16(v0) -> null_a__U16 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0, v1) -> null_a__U22 [0] a__U23(v0) -> null_a__U23 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0) -> null_a__U41 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1, v2) -> null_a__U62 [0] a__U63(v0, v1, v2) -> null_a__U63 [0] a__U64(v0, v1, v2) -> null_a__U64 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1, v2) -> null_A__U11 [0] A__U12(v0, v1, v2) -> null_A__U12 [0] A__U13(v0, v1, v2) -> null_A__U13 [0] A__U14(v0, v1, v2) -> null_A__U14 [0] A__U21(v0, v1) -> null_A__U21 [0] A__U51(v0, v1) -> null_A__U51 [0] A__U52(v0, v1) -> null_A__U52 [0] A__U61(v0, v1, v2) -> null_A__U61 [0] A__U62(v0, v1, v2) -> null_A__U62 [0] A__U63(v0, v1, v2) -> null_A__U63 [0] A__U64(v0, v1, v2) -> null_A__U64 [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__ISNATKIND(v0) -> null_A__ISNATKIND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] A__U15(v0, v1) -> null_A__U15 [0] A__U22(v0, v1) -> null_A__U22 [0] A__U31(v0, v1) -> null_A__U31 [0] The TRS has the following type information: A__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c:null_A__U11 tt :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c :: c2:null_A__U12 -> c42:c43:null_A__ISNATKIND -> c:null_A__U11 A__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c2:null_A__U12 a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNATKIND :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c42:c43:null_A__ISNATKIND c2 :: c4:null_A__U13 -> c42:c43:null_A__ISNATKIND -> c2:null_A__U12 A__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c4:null_A__U13 c4 :: c6:null_A__U14 -> c42:c43:null_A__ISNATKIND -> c4:null_A__U13 A__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c6:null_A__U14 c6 :: c8:null_A__U15 -> c38:c39:null_A__ISNAT -> c6:null_A__U14 A__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c8:null_A__U15 a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark A__ISNAT :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c38:c39:null_A__ISNAT A__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c12:null_A__U21 c12 :: c14:null_A__U22 -> c42:c43:null_A__ISNATKIND -> c12:null_A__U21 A__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c14:null_A__U22 A__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c24:null_A__U51 c24 :: c26:null_A__U52 -> c42:c43:null_A__ISNATKIND -> c24:null_A__U51 A__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c26:null_A__U52 c26 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c26:null_A__U52 MARK :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK A__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c28:null_A__U61 c28 :: c30:null_A__U62 -> c42:c43:null_A__ISNATKIND -> c28:null_A__U61 A__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c30:null_A__U62 c30 :: c32:null_A__U63 -> c38:c39:null_A__ISNAT -> c30:null_A__U62 A__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c32:null_A__U63 c32 :: c34:c35:null_A__U64 -> c42:c43:null_A__ISNATKIND -> c32:null_A__U63 A__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c34:c35:null_A__U64 c34 :: c45:c46:null_A__PLUS -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c34:c35:null_A__U64 A__PLUS :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c45:c46:null_A__PLUS mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c35 :: c45:c46:null_A__PLUS -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c34:c35:null_A__U64 plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c38 :: c:null_A__U11 -> c42:c43:null_A__ISNATKIND -> c38:c39:null_A__ISNAT s :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c39 :: c12:null_A__U21 -> c42:c43:null_A__ISNATKIND -> c38:c39:null_A__ISNAT c42 :: c18:null_A__U31 -> c42:c43:null_A__ISNATKIND -> c42:c43:null_A__ISNATKIND A__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> c18:null_A__U31 0 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c45 :: c24:null_A__U51 -> c38:c39:null_A__ISNAT -> c45:c46:null_A__PLUS c46 :: c28:null_A__U61 -> c38:c39:null_A__ISNAT -> c45:c46:null_A__PLUS U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c48 :: c:null_A__U11 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c49 :: c2:null_A__U12 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c50 :: c42:c43:null_A__ISNATKIND -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c51 :: c4:null_A__U13 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c52 :: c6:null_A__U14 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c53 :: c8:null_A__U15 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c54 :: c38:c39:null_A__ISNAT -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c56 :: c12:null_A__U21 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c57 :: c14:null_A__U22 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c59 :: c18:null_A__U31 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c62 :: c24:null_A__U51 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c63 :: c26:null_A__U52 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c64 :: c28:null_A__U61 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c65 :: c30:null_A__U62 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c66 :: c32:null_A__U63 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c67 :: c34:c35:null_A__U64 -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK c68 :: c45:c46:null_A__PLUS -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK c69 :: c45:c46:null_A__PLUS -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK c71 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK c8 :: c38:c39:null_A__ISNAT -> c8:null_A__U15 c14 :: c38:c39:null_A__ISNAT -> c14:null_A__U22 c18 :: c42:c43:null_A__ISNATKIND -> c18:null_A__U31 c43 :: c42:c43:null_A__ISNATKIND -> c42:c43:null_A__ISNATKIND U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c55 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c58 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c60 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark c61 :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK -> c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK a__U11 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U12 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U13 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark a__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark -> 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tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U14 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U15 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U16 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U21 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U22 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U23 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U31 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U32 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U41 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U51 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U52 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U61 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U62 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U63 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__U64 :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNat :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__isNatKind :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_a__plus :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_mark :: tt:plus:s:0:U11:U12:isNatKind:U13:U14:U15:isNat:U21:U22:U31:U51:U52:U61:U62:U63:U64:U16:U23:U32:U41:null_a__U11:null_a__U12:null_a__U13:null_a__U14:null_a__U15:null_a__U16:null_a__U21:null_a__U22:null_a__U23:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U63:null_a__U64:null_a__isNat:null_a__isNatKind:null_a__plus:null_mark null_A__U11 :: c:null_A__U11 null_A__U12 :: c2:null_A__U12 null_A__U13 :: c4:null_A__U13 null_A__U14 :: c6:null_A__U14 null_A__U21 :: c12:null_A__U21 null_A__U51 :: c24:null_A__U51 null_A__U52 :: c26:null_A__U52 null_A__U61 :: c28:null_A__U61 null_A__U62 :: c30:null_A__U62 null_A__U63 :: c32:null_A__U63 null_A__U64 :: c34:c35:null_A__U64 null_A__ISNAT :: c38:c39:null_A__ISNAT null_A__ISNATKIND :: c42:c43:null_A__ISNATKIND null_A__PLUS :: c45:c46:null_A__PLUS null_MARK :: c48:c49:c50:c51:c52:c53:c54:c56:c57:c59:c62:c63:c64:c65:c66:c67:c68:c69:c71:c55:c58:c60:c61:null_MARK null_A__U15 :: c8:null_A__U15 null_A__U22 :: c14:null_A__U22 null_A__U31 :: c18:null_A__U31 Rewrite Strategy: INNERMOST ---------------------------------------- (63) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U13 => 0 null_a__U14 => 0 null_a__U15 => 0 null_a__U16 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U23 => 0 null_a__U31 => 0 null_a__U32 => 0 null_a__U41 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U61 => 0 null_a__U62 => 0 null_a__U63 => 0 null_a__U64 => 0 null_a__isNat => 0 null_a__isNatKind => 0 null_a__plus => 0 null_mark => 0 null_A__U11 => 0 null_A__U12 => 0 null_A__U13 => 0 null_A__U14 => 0 null_A__U21 => 0 null_A__U51 => 0 null_A__U52 => 0 null_A__U61 => 0 null_A__U62 => 0 null_A__U63 => 0 null_A__U64 => 0 null_A__ISNAT => 0 null_A__ISNATKIND => 0 null_A__PLUS => 0 null_MARK => 0 null_A__U15 => 0 null_A__U22 => 0 null_A__U31 => 0 ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0), z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__isNatKind(z0), z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__U31(a__isNatKind(z0), z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__PLUS(z, z') -{ 1 }-> 1 + A__U61(a__isNat(z1), z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__isNat(z0), z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(a__isNatKind(z0), z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U12(z, z', z'') -{ 1 }-> 1 + A__U13(a__isNatKind(z1), z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U13(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U13(z, z', z'') -{ 1 }-> 1 + A__U14(a__isNatKind(z1), z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U14(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U14(z, z', z'') -{ 1 }-> 1 + A__U15(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U15(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U15(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U21(z, z') -{ 1 }-> 1 + A__U22(a__isNatKind(z0), z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U22(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U22(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U31(z, z') -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U51(z, z') -{ 1 }-> 1 + A__U52(a__isNatKind(z0), z0) + A__ISNATKIND(z0) :|: z = 1, z0 >= 0, z' = z0 A__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U52(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__isNatKind(z0), z0, z1) + A__ISNATKIND(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U62(z, z', z'') -{ 1 }-> 1 + A__U63(a__isNat(z1), z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U63(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U63(z, z', z'') -{ 1 }-> 1 + A__U64(a__isNatKind(z1), z0, z1) + A__ISNATKIND(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U64(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U64(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U64(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U63(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U22(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U15(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U14(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U13(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z', z'') -{ 0 }-> a__U12(a__isNatKind(z0), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U12(z, z', z'') -{ 0 }-> a__U13(a__isNatKind(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U13(z, z', z'') -{ 0 }-> a__U14(a__isNatKind(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U13(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U13(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U14(z, z', z'') -{ 0 }-> a__U15(a__isNat(z0), z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U14(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U14(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U15(z, z') -{ 0 }-> a__U16(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U15(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U15(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U16(z) -{ 0 }-> 1 :|: z = 1 a__U16(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U16(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__isNatKind(z0), z0) :|: z = 1, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z, z') -{ 0 }-> a__U23(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U22(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U22(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U23(z) -{ 0 }-> 1 :|: z = 1 a__U23(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U23(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__isNatKind(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 1 :|: z = 1 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z) -{ 0 }-> 1 :|: z = 1 a__U41(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U41(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__isNatKind(z0), z0) :|: z = 1, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U51(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U52(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__isNatKind(z0), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U62(z, z', z'') -{ 0 }-> a__U63(a__isNat(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U62(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U62(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U63(z, z', z'') -{ 0 }-> a__U64(a__isNatKind(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U63(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U63(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U64(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U64(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U64(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z0), z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__isNatKind(z0), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__U41(a__isNatKind(z0)) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__U31(a__isNatKind(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatKind(z) -{ 0 }-> 1 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U61(a__isNat(z1), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U51(a__isNat(z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U64(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U63(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U23(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U22(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U16(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U15(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U14(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U13(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, z0, z1) -> c(A__U12(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) by A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1), A__ISNATKIND(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1), A__ISNATKIND(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) S tuples: A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1), A__ISNATKIND(0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, z0, x1) -> c(A__U12(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3 Compound Symbols: c2_2, c4_2, c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) S tuples: A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3 Compound Symbols: c2_2, c4_2, c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, z0, z1) -> c2(A__U13(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) by A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0), A__ISNATKIND(0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, z0) -> c2(A__U13(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0), A__ISNATKIND(0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, z0) -> c2(A__U13(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) S tuples: A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0), A__ISNATKIND(0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, z0) -> c2(A__U13(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3 Compound Symbols: c4_2, c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) S tuples: A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3 Compound Symbols: c4_2, c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U13(tt, z0, z1) -> c4(A__U14(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) by A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0), A__ISNATKIND(0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, z0) -> c4(A__U14(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0), A__ISNATKIND(0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, z0) -> c4(A__U14(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) S tuples: A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0), A__ISNATKIND(0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, z0) -> c4(A__U14(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3 Compound Symbols: c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) S tuples: A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U14_3, A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3 Compound Symbols: c6_2, c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U14(tt, z0, z1) -> c6(A__U15(a__isNat(z0), z1), A__ISNAT(z0)) by A__U14(tt, 0, x1) -> c6(A__U15(tt, x1), A__ISNAT(0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, z0, x1) -> c6(A__U15(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1), A__ISNAT(0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, z0, x1) -> c6(A__U15(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1), A__ISNAT(0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, z0, x1) -> c6(A__U15(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3 Compound Symbols: c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) S tuples: A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U21_2, A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3 Compound Symbols: c12_2, c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, z0) -> c12(A__U22(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__U21(tt, 0) -> c12(A__U22(tt, 0), A__ISNATKIND(0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, z0) -> c12(A__U22(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, 0) -> c12(A__U22(tt, 0), A__ISNATKIND(0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, z0) -> c12(A__U22(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, 0) -> c12(A__U22(tt, 0), A__ISNATKIND(0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, z0) -> c12(A__U22(isNatKind(z0), z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2 Compound Symbols: c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) S tuples: A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U51_2, A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2 Compound Symbols: c24_2, c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, z0) -> c24(A__U52(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__U51(tt, 0) -> c24(A__U52(tt, 0), A__ISNATKIND(0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, z0) -> c24(A__U52(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, 0) -> c24(A__U52(tt, 0), A__ISNATKIND(0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, z0) -> c24(A__U52(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, 0) -> c24(A__U52(tt, 0), A__ISNATKIND(0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, z0) -> c24(A__U52(isNatKind(z0), z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2 Compound Symbols: c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2 Compound Symbols: c26_1, c28_2, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, z0, z1) -> c28(A__U62(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) by A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1), A__ISNATKIND(0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, z0, x1) -> c28(A__U62(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1), A__ISNATKIND(0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, z0, x1) -> c28(A__U62(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1), A__ISNATKIND(0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, z0, x1) -> c28(A__U62(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3 Compound Symbols: c26_1, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3 Compound Symbols: c26_1, c30_2, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U62(tt, z0, z1) -> c30(A__U63(a__isNat(z1), z0, z1), A__ISNAT(z1)) by A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0), A__ISNAT(0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, z0) -> c30(A__U63(isNat(z0), x0, z0), A__ISNAT(z0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0), A__ISNAT(0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, z0) -> c30(A__U63(isNat(z0), x0, z0), A__ISNAT(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0), A__ISNAT(0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, z0) -> c30(A__U63(isNat(z0), x0, z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3 Compound Symbols: c26_1, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U63_3, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3 Compound Symbols: c26_1, c32_2, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U63(tt, z0, z1) -> c32(A__U64(a__isNatKind(z1), z0, z1), A__ISNATKIND(z1)) by A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0), A__ISNATKIND(0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, z0) -> c32(A__U64(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0), A__ISNATKIND(0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, z0) -> c32(A__U64(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0), A__ISNATKIND(0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, z0) -> c32(A__U64(isNatKind(z0), x0, z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3 Compound Symbols: c26_1, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3 Compound Symbols: c26_1, c34_2, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U64(tt, z0, z1) -> c34(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, tt, x1) -> c34(A__PLUS(mark(x1), tt), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0)), MARK(tt)) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, tt, x1) -> c34(A__PLUS(mark(x1), tt), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0)), MARK(tt)) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, tt, x1) -> c34(A__PLUS(mark(x1), tt), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0)), MARK(tt)) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3 Compound Symbols: c26_1, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__U64_3, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3 Compound Symbols: c26_1, c35_2, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U64(tt, z0, z1) -> c35(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, tt, x1) -> c35(A__PLUS(mark(x1), tt), MARK(tt)) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0), MARK(0)) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, tt, x1) -> c35(A__PLUS(mark(x1), tt), MARK(tt)) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0), MARK(0)) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, tt, x1) -> c35(A__PLUS(mark(x1), tt), MARK(tt)) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0), MARK(0)) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3 Compound Symbols: c26_1, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U64(tt, tt, x1) -> c35(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0), MARK(0)) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0), MARK(0)) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3 Compound Symbols: c26_1, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3 Compound Symbols: c26_1, c38_2, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c38(A__U11(a__isNatKind(z0), z0, z1), A__ISNATKIND(z0)) by A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c38(A__U11(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c38(A__U11(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1), A__ISNATKIND(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(z0, x1)) -> c38(A__U11(isNatKind(z0), z0, x1), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3 Compound Symbols: c26_1, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3 Compound Symbols: c26_1, c39_2, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(s(z0)) -> c39(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__ISNAT(s(0)) -> c39(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c39(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(0)) -> c39(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c39(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(0)) -> c39(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c39(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1 Compound Symbols: c26_1, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1 Compound Symbols: c26_1, c42_2, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATKIND(plus(z0, z1)) -> c42(A__U31(a__isNatKind(z0), z1), A__ISNATKIND(z0)) by A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c42(A__U31(isNatKind(z0), x1), A__ISNATKIND(z0)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c42(A__U31(isNatKind(z0), x1), A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1), A__ISNATKIND(0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(z0, x1)) -> c42(A__U31(isNatKind(z0), x1), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1 Compound Symbols: c26_1, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1 Compound Symbols: c26_1, c45_2, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, 0) -> c45(A__U51(a__isNat(z0), z0), A__ISNAT(z0)) by A__PLUS(0, 0) -> c45(A__U51(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c45(A__U51(isNat(z0), z0), A__ISNAT(z0)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(0, 0) -> c45(A__U51(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c45(A__U51(isNat(z0), z0), A__ISNAT(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(0, 0) -> c45(A__U51(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c45(A__U51(isNat(z0), z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1 Compound Symbols: c26_1, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, A__PLUS_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1 Compound Symbols: c26_1, c46_2, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c46(A__U61(a__isNat(z1), z1, z0), A__ISNAT(z1)) by A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c46(A__U61(isNat(z0), z0, x0), A__ISNAT(z0)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c46(A__U61(isNat(z0), z0, x0), A__ISNAT(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c46(A__U61(isNat(z0), z0, x0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c48_2, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1, z2)) -> c48(A__U11(mark(z0), z1, z2), MARK(z0)) by MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c48(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c48(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c48(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c48(A__U11(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c48(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U11(0, x1, x2)) -> c48(A__U11(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1, x2)) -> c48(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c48(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2), MARK(tt)) MARK(U11(s(z0), x1, x2)) -> c48(A__U11(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(isNatKind(z0), x1, x2)) -> c48(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(isNat(z0), x1, x2)) -> c48(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1 ---------------------------------------- (137) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c49_2, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0, z1, z2)) -> c49(A__U12(mark(z0), z1, z2), MARK(z0)) by MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c49(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U12(0, x1, x2)) -> c49(A__U12(0, x1, x2), MARK(0)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c49(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U12(0, x1, x2)) -> c49(A__U12(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c49(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U12(0, x1, x2)) -> c49(A__U12(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2 ---------------------------------------- (141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U12(0, x1, x2)) -> c49(A__U12(0, x1, x2), MARK(0)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c49(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2), MARK(tt)) MARK(U12(s(z0), x1, x2)) -> c49(A__U12(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(isNatKind(z0), x1, x2)) -> c49(A__U12(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(isNat(z0), x1, x2)) -> c49(A__U12(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1 ---------------------------------------- (145) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c51_2, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U13(z0, z1, z2)) -> c51(A__U13(mark(z0), z1, z2), MARK(z0)) by MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2), MARK(tt)) MARK(U13(s(z0), x1, x2)) -> c51(A__U13(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U13(0, x1, x2)) -> c51(A__U13(0, x1, x2), MARK(0)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2), MARK(tt)) MARK(U13(s(z0), x1, x2)) -> c51(A__U13(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U13(0, x1, x2)) -> c51(A__U13(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2), MARK(tt)) MARK(U13(s(z0), x1, x2)) -> c51(A__U13(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U13(0, x1, x2)) -> c51(A__U13(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U13(0, x1, x2)) -> c51(A__U13(0, x1, x2), MARK(0)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2), MARK(tt)) MARK(U13(s(z0), x1, x2)) -> c51(A__U13(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2), MARK(tt)) MARK(U13(s(z0), x1, x2)) -> c51(A__U13(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(isNatKind(z0), x1, x2)) -> c51(A__U13(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(isNat(z0), x1, x2)) -> c51(A__U13(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1 ---------------------------------------- (153) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c52_2, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U14(z0, z1, z2)) -> c52(A__U14(mark(z0), z1, z2), MARK(z0)) by MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2), MARK(tt)) MARK(U14(s(z0), x1, x2)) -> c52(A__U14(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U14(0, x1, x2)) -> c52(A__U14(0, x1, x2), MARK(0)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2), MARK(tt)) MARK(U14(s(z0), x1, x2)) -> c52(A__U14(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U14(0, x1, x2)) -> c52(A__U14(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2), MARK(tt)) MARK(U14(s(z0), x1, x2)) -> c52(A__U14(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U14(0, x1, x2)) -> c52(A__U14(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U14(0, x1, x2)) -> c52(A__U14(0, x1, x2), MARK(0)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2), MARK(tt)) MARK(U14(s(z0), x1, x2)) -> c52(A__U14(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2), MARK(tt)) MARK(U14(s(z0), x1, x2)) -> c52(A__U14(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(isNatKind(z0), x1, x2)) -> c52(A__U14(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(isNat(z0), x1, x2)) -> c52(A__U14(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1 ---------------------------------------- (161) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c53_2, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U15(z0, z1)) -> c53(A__U15(mark(z0), z1), MARK(z0)) by MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1), MARK(tt)) MARK(U15(s(z0), x1)) -> c53(A__U15(s(mark(z0)), x1), MARK(s(z0))) MARK(U15(0, x1)) -> c53(A__U15(0, x1), MARK(0)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1), MARK(tt)) MARK(U15(s(z0), x1)) -> c53(A__U15(s(mark(z0)), x1), MARK(s(z0))) MARK(U15(0, x1)) -> c53(A__U15(0, x1), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1), MARK(tt)) MARK(U15(s(z0), x1)) -> c53(A__U15(s(mark(z0)), x1), MARK(s(z0))) MARK(U15(0, x1)) -> c53(A__U15(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2 ---------------------------------------- (165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U15(0, x1)) -> c53(A__U15(0, x1), MARK(0)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1), MARK(tt)) MARK(U15(s(z0), x1)) -> c53(A__U15(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1), MARK(tt)) MARK(U15(s(z0), x1)) -> c53(A__U15(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(isNatKind(z0), x1)) -> c53(A__U15(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(isNat(z0), x1)) -> c53(A__U15(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1 ---------------------------------------- (169) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c56_2, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) by MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1 ---------------------------------------- (177) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c57_2, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U22(z0, z1)) -> c57(A__U22(mark(z0), z1), MARK(z0)) by MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1), MARK(tt)) MARK(U22(s(z0), x1)) -> c57(A__U22(s(mark(z0)), x1), MARK(s(z0))) MARK(U22(0, x1)) -> c57(A__U22(0, x1), MARK(0)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1), MARK(tt)) MARK(U22(s(z0), x1)) -> c57(A__U22(s(mark(z0)), x1), MARK(s(z0))) MARK(U22(0, x1)) -> c57(A__U22(0, x1), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1), MARK(tt)) MARK(U22(s(z0), x1)) -> c57(A__U22(s(mark(z0)), x1), MARK(s(z0))) MARK(U22(0, x1)) -> c57(A__U22(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U22(0, x1)) -> c57(A__U22(0, x1), MARK(0)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1), MARK(tt)) MARK(U22(s(z0), x1)) -> c57(A__U22(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1), MARK(tt)) MARK(U22(s(z0), x1)) -> c57(A__U22(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(isNatKind(z0), x1)) -> c57(A__U22(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(isNat(z0), x1)) -> c57(A__U22(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1 ---------------------------------------- (185) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c59_2, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, 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c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), 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c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) 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c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), 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MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2 ---------------------------------------- (189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, 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c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) 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c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1 ---------------------------------------- (193) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c62_2, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U51(z0, z1)) -> c62(A__U51(mark(z0), z1), MARK(z0)) by MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c62(A__U51(s(mark(z0)), x1), MARK(s(z0))) MARK(U51(0, x1)) -> c62(A__U51(0, x1), MARK(0)) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) 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c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c62(A__U51(s(mark(z0)), x1), MARK(s(z0))) MARK(U51(0, x1)) -> c62(A__U51(0, x1), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), 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c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) 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c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c62(A__U51(s(mark(z0)), x1), MARK(s(z0))) MARK(U51(0, x1)) -> c62(A__U51(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2 ---------------------------------------- (197) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U51(0, x1)) -> c62(A__U51(0, x1), MARK(0)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, 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c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c62(A__U51(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, 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MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> 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c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) 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c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c62(A__U51(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c63_2, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U52(z0, z1)) -> c63(A__U52(mark(z0), z1), MARK(z0)) by MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c63(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(0, x1)) -> c63(A__U52(0, x1), MARK(0)) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c63(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(0, x1)) -> c63(A__U52(0, x1), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c63(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(0, x1)) -> c63(A__U52(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2 ---------------------------------------- (203) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U52(0, x1)) -> c63(A__U52(0, x1), MARK(0)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) 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MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), 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MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c63(A__U52(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), 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c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c63(A__U52(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c64_2, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U61(z0, z1, z2)) -> c64(A__U61(mark(z0), z1, z2), MARK(z0)) by MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c64(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U61(0, x1, x2)) -> c64(A__U61(0, x1, x2), MARK(0)) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> 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MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> 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MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> 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z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c64(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U61(0, x1, x2)) -> c64(A__U61(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c64(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U61(0, x1, x2)) -> c64(A__U61(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2 ---------------------------------------- (209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U61(0, x1, x2)) -> c64(A__U61(0, x1, x2), MARK(0)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, 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MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, 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c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> 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MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) 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c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c64(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c64(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, 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MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c65_2, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U62(z0, z1, z2)) -> c65(A__U62(mark(z0), z1, z2), MARK(z0)) by MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2), MARK(tt)) MARK(U62(s(z0), x1, x2)) -> c65(A__U62(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U62(0, x1, x2)) -> c65(A__U62(0, x1, x2), MARK(0)) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2), MARK(tt)) MARK(U62(s(z0), x1, x2)) -> c65(A__U62(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U62(0, x1, x2)) -> c65(A__U62(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2), MARK(tt)) MARK(U62(s(z0), x1, x2)) -> c65(A__U62(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U62(0, x1, x2)) -> c65(A__U62(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2 ---------------------------------------- (215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U62(0, x1, x2)) -> c65(A__U62(0, x1, x2), MARK(0)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), 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c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), 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MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> 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x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2), MARK(tt)) MARK(U62(s(z0), x1, x2)) -> c65(A__U62(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, 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c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2), MARK(tt)) MARK(U62(s(z0), x1, x2)) -> c65(A__U62(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), 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c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) 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c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), 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MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c66_2, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U63(z0, z1, z2)) -> c66(A__U63(mark(z0), z1, z2), MARK(z0)) by MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2), MARK(tt)) MARK(U63(s(z0), x1, x2)) -> c66(A__U63(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U63(0, x1, x2)) -> c66(A__U63(0, x1, x2), MARK(0)) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2), MARK(tt)) MARK(U63(s(z0), x1, x2)) -> c66(A__U63(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U63(0, x1, x2)) -> c66(A__U63(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2), MARK(tt)) MARK(U63(s(z0), x1, x2)) -> c66(A__U63(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U63(0, x1, x2)) -> c66(A__U63(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2 ---------------------------------------- (221) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U63(0, x1, x2)) -> c66(A__U63(0, x1, x2), MARK(0)) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2), MARK(tt)) MARK(U63(s(z0), x1, x2)) -> c66(A__U63(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> 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MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2), MARK(tt)) MARK(U63(s(z0), x1, x2)) -> c66(A__U63(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, 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MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, 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c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> 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MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) 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c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, 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MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c67_2, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U64(z0, z1, z2)) -> c67(A__U64(mark(z0), z1, z2), MARK(z0)) by MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2), MARK(tt)) MARK(U64(s(z0), x1, x2)) -> c67(A__U64(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U64(0, x1, x2)) -> c67(A__U64(0, x1, x2), MARK(0)) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2), MARK(tt)) MARK(U64(s(z0), x1, x2)) -> c67(A__U64(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U64(0, x1, x2)) -> c67(A__U64(0, x1, x2), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> 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c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) 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c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), 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MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> 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x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2), MARK(tt)) MARK(U64(s(z0), x1, x2)) -> c67(A__U64(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U64(0, x1, x2)) -> c67(A__U64(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2 ---------------------------------------- (227) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U64(0, x1, x2)) -> c67(A__U64(0, x1, x2), MARK(0)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, 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c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2), MARK(tt)) MARK(U64(s(z0), x1, x2)) -> c67(A__U64(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, 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MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, 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MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2), MARK(tt)) MARK(U64(s(z0), x1, x2)) -> c67(A__U64(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, 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c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c68_2, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c68(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c68(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, 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MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c68(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, 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c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c68(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c69_2, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1 ---------------------------------------- (235) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c69(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c69(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c69(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) 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c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, 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x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) 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c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c69(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2 ---------------------------------------- (237) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c69(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, 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c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, 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MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> 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MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2 ---------------------------------------- (239) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1 ---------------------------------------- (241) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) by A__U11(tt, plus(x0, z1), x2) -> c(A__U12(U31(a__isNatKind(x0), z1), plus(x0, z1), x2), A__ISNATKIND(plus(x0, z1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, 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c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) 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MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(x0, z1), x2) -> c(A__U12(U31(a__isNatKind(x0), z1), plus(x0, z1), x2), A__ISNATKIND(plus(x0, z1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, 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MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> 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MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(x0, z1), x2) -> c(A__U12(U31(a__isNatKind(x0), z1), plus(x0, z1), x2), A__ISNATKIND(plus(x0, z1))) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1 ---------------------------------------- (243) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), 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c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), 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MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> 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x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> 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MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_2, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1 ---------------------------------------- (245) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) by A__U11(tt, s(x0), x1) -> c(A__U12(U41(a__isNatKind(x0)), s(x0), x1), A__ISNATKIND(s(x0))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> 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MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(x0), x1) -> c(A__U12(U41(a__isNatKind(x0)), s(x0), x1), A__ISNATKIND(s(x0))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(x0), x1) -> c(A__U12(U41(a__isNatKind(x0)), s(x0), x1), A__ISNATKIND(s(x0))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2 ---------------------------------------- (247) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> 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z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), 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MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2 ---------------------------------------- (249) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, plus(z0, z1)) -> c2(A__U13(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) by A__U12(tt, x0, plus(x1, z1)) -> c2(A__U13(U31(a__isNatKind(x1), z1), x0, plus(x1, z1)), A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) ---------------------------------------- (250) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), 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c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), 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MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__U13(U31(a__isNatKind(x1), z1), x0, plus(x1, z1)), A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, 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c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__U13(U31(a__isNatKind(x1), z1), x0, plus(x1, z1)), A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2 ---------------------------------------- (251) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (252) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), 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c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> 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MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) 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z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_2, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2 ---------------------------------------- (253) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) by A__U12(tt, x0, s(x1)) -> c2(A__U13(U41(a__isNatKind(x1)), x0, s(x1)), A__ISNATKIND(s(x1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) ---------------------------------------- (254) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> 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MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(x1)) -> c2(A__U13(U41(a__isNatKind(x1)), x0, s(x1)), A__ISNATKIND(s(x1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(x1)) -> c2(A__U13(U41(a__isNatKind(x1)), x0, s(x1)), A__ISNATKIND(s(x1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2, c2_2 ---------------------------------------- (255) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (256) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, s(x1)) -> c2(A__ISNATKIND(s(x1))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) 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c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, 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c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, s(x1)) -> c2(A__ISNATKIND(s(x1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2, c2_2 ---------------------------------------- (257) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U13(tt, x0, plus(z0, z1)) -> c4(A__U14(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) by A__U13(tt, x0, plus(x1, z1)) -> c4(A__U14(U31(a__isNatKind(x1), z1), x0, plus(x1, z1)), A__ISNATKIND(plus(x1, z1))) A__U13(tt, x0, plus(0, x2)) -> c4(A__U14(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U13(tt, x0, plus(plus(z0, z1), x2)) -> c4(A__U14(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U13(tt, x0, plus(s(z0), x2)) -> c4(A__U14(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U13(tt, x0, plus(z0, x2)) -> c4(A__U14(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) ---------------------------------------- (258) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, s(x1)) -> c2(A__ISNATKIND(s(x1))) A__U13(tt, x0, plus(x1, z1)) -> c4(A__U14(U31(a__isNatKind(x1), z1), x0, plus(x1, z1)), A__ISNATKIND(plus(x1, z1))) A__U13(tt, x0, plus(0, x2)) -> c4(A__U14(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U13(tt, x0, plus(plus(z0, z1), x2)) -> c4(A__U14(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U13(tt, x0, plus(s(z0), x2)) -> c4(A__U14(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U13(tt, x0, plus(z0, x2)) -> c4(A__U14(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, 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c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), x1)) -> c10(MARK(isNat(z0))) MARK(U22(U11(z0, z1, z2), x1)) -> c57(A__U22(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U22(U12(z0, z1, z2), x1)) -> c57(A__U22(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U22(U13(z0, z1, z2), x1)) -> c57(A__U22(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U22(U14(z0, z1, z2), x1)) -> c57(A__U22(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U22(U15(z0, z1), x1)) -> c57(A__U22(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U22(U16(z0), x1)) -> c57(A__U22(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U22(U21(z0, z1), x1)) -> c57(A__U22(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U22(U22(z0, z1), x1)) -> c57(A__U22(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U22(U23(z0), x1)) -> c57(A__U22(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U22(U31(z0, z1), x1)) -> c57(A__U22(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U22(U32(z0), x1)) -> c57(A__U22(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, s(x1)) -> c2(A__ISNATKIND(s(x1))) A__U13(tt, x0, plus(x1, z1)) -> c4(A__U14(U31(a__isNatKind(x1), z1), x0, plus(x1, z1)), A__ISNATKIND(plus(x1, z1))) A__U13(tt, x0, plus(0, x2)) -> c4(A__U14(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U13(tt, x0, plus(plus(z0, z1), x2)) -> c4(A__U14(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U13(tt, x0, plus(s(z0), x2)) -> c4(A__U14(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U13(tt, x0, plus(z0, x2)) -> c4(A__U14(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2, c2_2 ---------------------------------------- (259) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (260) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__isNatKind(z0), z0, z1) a__U11(z0, z1, z2) -> U11(z0, z1, z2) a__U12(tt, z0, z1) -> a__U13(a__isNatKind(z1), z0, z1) a__U12(z0, z1, z2) -> U12(z0, z1, z2) a__U13(tt, z0, z1) -> a__U14(a__isNatKind(z1), z0, z1) a__U13(z0, z1, z2) -> U13(z0, z1, z2) a__U14(tt, z0, z1) -> a__U15(a__isNat(z0), z1) a__U14(z0, z1, z2) -> U14(z0, z1, z2) a__U15(tt, z0) -> a__U16(a__isNat(z0)) a__U15(z0, z1) -> U15(z0, z1) a__U16(tt) -> tt a__U16(z0) -> U16(z0) a__U21(tt, z0) -> a__U22(a__isNatKind(z0), z0) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt, z0) -> a__U23(a__isNat(z0)) a__U22(z0, z1) -> U22(z0, z1) a__U23(tt) -> tt a__U23(z0) -> U23(z0) a__U31(tt, z0) -> a__U32(a__isNatKind(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt) -> tt a__U41(z0) -> U41(z0) a__U51(tt, z0) -> a__U52(a__isNatKind(z0), z0) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt, z0) -> mark(z0) a__U52(z0, z1) -> U52(z0, z1) a__U61(tt, z0, z1) -> a__U62(a__isNatKind(z0), z0, z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0, z1) -> a__U63(a__isNat(z1), z0, z1) a__U62(z0, z1, z2) -> U62(z0, z1, z2) a__U63(tt, z0, z1) -> a__U64(a__isNatKind(z1), z0, z1) a__U63(z0, z1, z2) -> U63(z0, z1, z2) a__U64(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U64(z0, z1, z2) -> U64(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNatKind(z0), z0, z1) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatKind(0) -> tt a__isNatKind(plus(z0, z1)) -> a__U31(a__isNatKind(z0), z1) a__isNatKind(s(z0)) -> a__U41(a__isNatKind(z0)) a__isNatKind(z0) -> isNatKind(z0) a__plus(z0, 0) -> a__U51(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U61(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(U13(z0, z1, z2)) -> a__U13(mark(z0), z1, z2) mark(U14(z0, z1, z2)) -> a__U14(mark(z0), z1, z2) mark(U15(z0, z1)) -> a__U15(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(U16(z0)) -> a__U16(mark(z0)) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0, z1)) -> a__U22(mark(z0), z1) mark(U23(z0)) -> a__U23(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0)) -> a__U41(mark(z0)) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1, z2)) -> a__U62(mark(z0), z1, z2) mark(U63(z0, z1, z2)) -> a__U63(mark(z0), z1, z2) mark(U64(z0, z1, z2)) -> a__U64(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__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U13(U63(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U13(U64(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U13(plus(z0, z1), x1, x2)) -> c51(A__U13(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U13(tt, x1, x2)) -> c51(A__U13(tt, x1, x2)) MARK(U13(s(z0), x1, x2)) -> c51(MARK(s(z0))) MARK(U13(isNatKind(z0), x1, x2)) -> c5(A__U13(a__isNatKind(z0), x1, x2)) MARK(U13(isNatKind(z0), x1, x2)) -> c5(MARK(isNatKind(z0))) MARK(U13(isNat(z0), x1, x2)) -> c5(A__U13(a__isNat(z0), x1, x2)) MARK(U13(isNat(z0), x1, x2)) -> c5(MARK(isNat(z0))) MARK(U14(U11(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U14(U12(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U14(U13(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> c53(A__U15(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U15(U12(z0, z1, z2), x1)) -> c53(A__U15(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U15(U13(z0, z1, z2), x1)) -> c53(A__U15(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U15(U14(z0, z1, z2), x1)) -> c53(A__U15(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U15(U15(z0, z1), x1)) -> c53(A__U15(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U15(U16(z0), x1)) -> c53(A__U15(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U15(U21(z0, z1), x1)) -> c53(A__U15(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U15(U22(z0, z1), x1)) -> c53(A__U15(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U15(U23(z0), x1)) -> c53(A__U15(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U15(U31(z0, z1), x1)) -> c53(A__U15(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U15(U32(z0), x1)) -> c53(A__U15(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U15(U41(z0), x1)) -> c53(A__U15(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), 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MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, 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MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> 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x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, s(x1)) -> c2(A__ISNATKIND(s(x1))) A__U13(tt, x0, plus(0, x2)) -> c4(A__U14(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U13(tt, x0, plus(plus(z0, z1), x2)) -> c4(A__U14(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U13(tt, x0, plus(s(z0), x2)) -> c4(A__U14(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U13(tt, x0, plus(z0, x2)) -> c4(A__U14(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U13(tt, x0, plus(x1, z1)) -> c4(A__ISNATKIND(plus(x1, z1))) S tuples: A__U52(tt, z0) -> c26(MARK(z0)) MARK(isNatKind(z0)) -> c50(A__ISNATKIND(z0)) MARK(isNat(z0)) -> c54(A__ISNAT(z0)) MARK(s(z0)) -> c71(MARK(z0)) A__U15(tt, z0) -> c8(A__ISNAT(z0)) A__U22(tt, z0) -> c14(A__ISNAT(z0)) A__U31(tt, z0) -> c18(A__ISNATKIND(z0)) A__ISNATKIND(s(z0)) -> c43(A__ISNATKIND(z0)) MARK(U16(z0)) -> c55(MARK(z0)) MARK(U23(z0)) -> c58(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U41(z0)) -> c61(MARK(z0)) A__U11(tt, 0, x1) -> c(A__U12(tt, 0, x1)) A__U11(tt, z0, x1) -> c(A__ISNATKIND(z0)) A__U12(tt, x0, 0) -> c2(A__U13(tt, x0, 0)) A__U12(tt, x0, z0) -> c2(A__ISNATKIND(z0)) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, 0) -> c4(A__U14(tt, x0, 0)) A__U13(tt, x0, z0) -> c4(A__ISNATKIND(z0)) A__U14(tt, plus(z0, z1), x1) -> c6(A__U15(a__U11(a__isNatKind(z0), z0, z1), x1), A__ISNAT(plus(z0, z1))) A__U14(tt, s(z0), x1) -> c6(A__U15(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U14(tt, 0, x1) -> c6(A__U15(tt, x1)) A__U14(tt, z0, x1) -> c6(A__ISNAT(z0)) A__U21(tt, plus(z0, z1)) -> c12(A__U22(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U21(tt, s(z0)) -> c12(A__U22(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U21(tt, 0) -> c12(A__U22(tt, 0)) A__U21(tt, z0) -> c12(A__ISNATKIND(z0)) A__U51(tt, plus(z0, z1)) -> c24(A__U52(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U51(tt, s(z0)) -> c24(A__U52(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__U51(tt, 0) -> c24(A__U52(tt, 0)) A__U51(tt, z0) -> c24(A__ISNATKIND(z0)) A__U61(tt, plus(z0, z1), x1) -> c28(A__U62(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__U61(tt, s(z0), x1) -> c28(A__U62(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U61(tt, 0, x1) -> c28(A__U62(tt, 0, x1)) A__U61(tt, z0, x1) -> c28(A__ISNATKIND(z0)) A__U62(tt, x0, plus(z0, z1)) -> c30(A__U63(a__U11(a__isNatKind(z0), z0, z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U62(tt, x0, s(z0)) -> c30(A__U63(a__U21(a__isNatKind(z0), z0), x0, s(z0)), A__ISNAT(s(z0))) A__U62(tt, x0, 0) -> c30(A__U63(tt, x0, 0)) A__U62(tt, x0, z0) -> c30(A__ISNAT(z0)) A__U63(tt, x0, plus(z0, z1)) -> c32(A__U64(a__U31(a__isNatKind(z0), z1), x0, plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__U63(tt, x0, s(z0)) -> c32(A__U64(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U63(tt, x0, 0) -> c32(A__U64(tt, x0, 0)) A__U63(tt, x0, z0) -> c32(A__ISNATKIND(z0)) A__U64(tt, U11(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U12(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, isNatKind(z0), x1) -> c34(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) A__U64(tt, U13(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U14(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U15(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(x1)) A__U64(tt, isNat(z0), x1) -> c34(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U64(tt, U16(z0), x1) -> c34(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(x1)) A__U64(tt, U21(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) A__U64(tt, U22(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(x1)) A__U64(tt, U23(z0), x1) -> c34(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(x1)) A__U64(tt, U31(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U64(tt, U32(z0), x1) -> c34(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U64(tt, U41(z0), x1) -> c34(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(x1)) A__U64(tt, U51(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(x1)) A__U64(tt, U52(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(x1)) A__U64(tt, U61(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U62(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U63(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, U64(z0, z1, z2), x1) -> c34(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(x1)) A__U64(tt, plus(z0, z1), x1) -> c34(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U64(tt, s(z0), x1) -> c34(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U64(tt, 0, x1) -> c34(A__PLUS(mark(x1), 0), MARK(x1)) A__U64(tt, x0, U11(z0, z1, z2)) -> c34(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) A__U64(tt, x0, U12(z0, z1, z2)) -> c34(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) A__U64(tt, x0, isNatKind(z0)) -> c34(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) A__U64(tt, x0, U13(z0, z1, z2)) -> c34(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(U13(z0, z1, z2))) A__U64(tt, x0, U14(z0, z1, z2)) -> c34(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(U14(z0, z1, z2))) A__U64(tt, x0, U15(z0, z1)) -> c34(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(U15(z0, z1))) A__U64(tt, x0, isNat(z0)) -> c34(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U64(tt, x0, U16(z0)) -> c34(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(U16(z0))) A__U64(tt, x0, U21(z0, z1)) -> c34(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) A__U64(tt, x0, U22(z0, z1)) -> c34(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(U22(z0, z1))) A__U64(tt, x0, U23(z0)) -> c34(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(U23(z0))) A__U64(tt, x0, U31(z0, z1)) -> c34(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U64(tt, x0, U32(z0)) -> c34(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U64(tt, x0, U41(z0)) -> c34(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(U41(z0))) A__U64(tt, x0, U51(z0, z1)) -> c34(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(U51(z0, z1))) A__U64(tt, x0, U52(z0, z1)) -> c34(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(U52(z0, z1))) A__U64(tt, x0, U61(z0, z1, z2)) -> c34(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(U61(z0, z1, z2))) A__U64(tt, x0, U62(z0, z1, z2)) -> c34(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(U62(z0, z1, z2))) A__U64(tt, x0, U63(z0, z1, z2)) -> c34(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(U63(z0, z1, z2))) A__U64(tt, x0, U64(z0, z1, z2)) -> c34(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(U64(z0, z1, z2))) A__U64(tt, x0, plus(z0, z1)) -> c34(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U64(tt, x0, s(z0)) -> c34(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U64(tt, tt, x1) -> c34(MARK(x1)) A__U64(tt, x0, tt) -> c34(A__PLUS(tt, mark(x0))) A__U64(tt, x0, 0) -> c34(A__PLUS(0, mark(x0))) A__U64(tt, U11(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) A__U64(tt, U12(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) A__U64(tt, isNatKind(z0), x1) -> c35(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0))) A__U64(tt, U13(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) A__U64(tt, U14(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) A__U64(tt, U15(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) A__U64(tt, isNat(z0), x1) -> c35(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U64(tt, U16(z0), x1) -> c35(A__PLUS(mark(x1), a__U16(mark(z0))), MARK(U16(z0))) A__U64(tt, U21(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U64(tt, U22(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) A__U64(tt, U23(z0), x1) -> c35(A__PLUS(mark(x1), a__U23(mark(z0))), MARK(U23(z0))) A__U64(tt, U31(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U64(tt, U32(z0), x1) -> c35(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U64(tt, U41(z0), x1) -> c35(A__PLUS(mark(x1), a__U41(mark(z0))), MARK(U41(z0))) A__U64(tt, U51(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U64(tt, U52(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U64(tt, U61(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U64(tt, U62(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) A__U64(tt, U63(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) A__U64(tt, U64(z0, z1, z2), x1) -> c35(A__PLUS(mark(x1), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) A__U64(tt, plus(z0, z1), x1) -> c35(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U64(tt, s(z0), x1) -> c35(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U64(tt, x0, U11(z0, z1, z2)) -> c35(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U12(z0, z1, z2)) -> c35(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, isNatKind(z0)) -> c35(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U13(z0, z1, z2)) -> c35(A__PLUS(a__U13(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U14(z0, z1, z2)) -> c35(A__PLUS(a__U14(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U15(z0, z1)) -> c35(A__PLUS(a__U15(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, isNat(z0)) -> c35(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U64(tt, x0, U16(z0)) -> c35(A__PLUS(a__U16(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U21(z0, z1)) -> c35(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U22(z0, z1)) -> c35(A__PLUS(a__U22(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U23(z0)) -> c35(A__PLUS(a__U23(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U31(z0, z1)) -> c35(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U32(z0)) -> c35(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U41(z0)) -> c35(A__PLUS(a__U41(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, U51(z0, z1)) -> c35(A__PLUS(a__U51(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U52(z0, z1)) -> c35(A__PLUS(a__U52(mark(z0), z1), mark(x0)), MARK(x0)) A__U64(tt, x0, U61(z0, z1, z2)) -> c35(A__PLUS(a__U61(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U62(z0, z1, z2)) -> c35(A__PLUS(a__U62(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U63(z0, z1, z2)) -> c35(A__PLUS(a__U63(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, U64(z0, z1, z2)) -> c35(A__PLUS(a__U64(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U64(tt, x0, plus(z0, z1)) -> c35(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U64(tt, x0, tt) -> c35(A__PLUS(tt, mark(x0)), MARK(x0)) A__U64(tt, x0, s(z0)) -> c35(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U64(tt, x0, 0) -> c35(A__PLUS(0, mark(x0)), MARK(x0)) A__U64(tt, 0, x1) -> c35(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c38(A__U11(a__U31(a__isNatKind(z0), z1), plus(z0, z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c38(A__U11(a__U41(a__isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__ISNAT(plus(0, x1)) -> c38(A__U11(tt, 0, x1)) A__ISNAT(plus(z0, x1)) -> c38(A__ISNATKIND(z0)) A__ISNAT(s(plus(z0, z1))) -> c39(A__U21(a__U31(a__isNatKind(z0), z1), plus(z0, z1)), A__ISNATKIND(plus(z0, z1))) A__ISNAT(s(s(z0))) -> c39(A__U21(a__U41(a__isNatKind(z0)), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c39(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c39(A__ISNATKIND(z0)) A__ISNATKIND(plus(plus(z0, z1), x1)) -> c42(A__U31(a__U31(a__isNatKind(z0), z1), x1), A__ISNATKIND(plus(z0, z1))) A__ISNATKIND(plus(s(z0), x1)) -> c42(A__U31(a__U41(a__isNatKind(z0)), x1), A__ISNATKIND(s(z0))) A__ISNATKIND(plus(0, x1)) -> c42(A__U31(tt, x1)) A__ISNATKIND(plus(z0, x1)) -> c42(A__ISNATKIND(z0)) A__PLUS(plus(z0, z1), 0) -> c45(A__U51(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c45(A__U51(a__U21(a__isNatKind(z0), z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c45(A__U51(tt, 0)) A__PLUS(z0, 0) -> c45(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c46(A__U61(a__U11(a__isNatKind(z0), z0, z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c46(A__U61(a__U21(a__isNatKind(z0), z0), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c46(A__U61(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c46(A__ISNAT(z0)) MARK(U11(U11(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U11(U12(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U11(U13(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U11(U14(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U11(U15(z0, z1), x1, x2)) -> c48(A__U11(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U11(U16(z0), x1, x2)) -> c48(A__U11(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U11(U21(z0, z1), x1, x2)) -> c48(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U11(U22(z0, z1), x1, x2)) -> c48(A__U11(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U11(U23(z0), x1, x2)) -> c48(A__U11(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U11(U31(z0, z1), x1, x2)) -> c48(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1, x2)) -> c48(A__U11(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U11(U41(z0), x1, x2)) -> c48(A__U11(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U11(U51(z0, z1), x1, x2)) -> c48(A__U11(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U11(U52(z0, z1), x1, x2)) -> c48(A__U11(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U11(U61(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U11(U63(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U11(U64(z0, z1, z2), x1, x2)) -> c48(A__U11(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U11(plus(z0, z1), x1, x2)) -> c48(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U11(tt, x1, x2)) -> c48(A__U11(tt, x1, x2)) MARK(U11(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U11(isNatKind(z0), x1, x2)) -> c1(A__U11(a__isNatKind(z0), x1, x2)) MARK(U11(isNatKind(z0), x1, x2)) -> c1(MARK(isNatKind(z0))) MARK(U11(isNat(z0), x1, x2)) -> c1(A__U11(a__isNat(z0), x1, x2)) MARK(U11(isNat(z0), x1, x2)) -> c1(MARK(isNat(z0))) MARK(U12(U11(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U12(U12(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U12(U13(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U12(U14(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U12(U15(z0, z1), x1, x2)) -> c49(A__U12(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U12(U16(z0), x1, x2)) -> c49(A__U12(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U12(U21(z0, z1), x1, x2)) -> c49(A__U12(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U12(U22(z0, z1), x1, x2)) -> c49(A__U12(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U12(U23(z0), x1, x2)) -> c49(A__U12(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U12(U31(z0, z1), x1, x2)) -> c49(A__U12(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U12(U32(z0), x1, x2)) -> c49(A__U12(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U12(U41(z0), x1, x2)) -> c49(A__U12(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U12(U51(z0, z1), x1, x2)) -> c49(A__U12(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U12(U52(z0, z1), x1, x2)) -> c49(A__U12(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U12(U61(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U12(U62(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U12(U63(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U12(U64(z0, z1, z2), x1, x2)) -> c49(A__U12(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U12(plus(z0, z1), x1, x2)) -> c49(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U12(tt, x1, x2)) -> c49(A__U12(tt, x1, x2)) MARK(U12(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(U12(isNatKind(z0), x1, x2)) -> c3(A__U12(a__isNatKind(z0), x1, x2)) MARK(U12(isNatKind(z0), x1, x2)) -> c3(MARK(isNatKind(z0))) MARK(U12(isNat(z0), x1, x2)) -> c3(A__U12(a__isNat(z0), x1, x2)) MARK(U12(isNat(z0), x1, x2)) -> c3(MARK(isNat(z0))) MARK(U13(U11(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U13(U12(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U13(U13(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U13(U14(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U13(U15(z0, z1), x1, x2)) -> c51(A__U13(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U13(U16(z0), x1, x2)) -> c51(A__U13(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U13(U21(z0, z1), x1, x2)) -> c51(A__U13(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U13(U22(z0, z1), x1, x2)) -> c51(A__U13(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U13(U23(z0), x1, x2)) -> c51(A__U13(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U13(U31(z0, z1), x1, x2)) -> c51(A__U13(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U13(U32(z0), x1, x2)) -> c51(A__U13(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U13(U41(z0), x1, x2)) -> c51(A__U13(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U13(U51(z0, z1), x1, x2)) -> c51(A__U13(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U13(U52(z0, z1), x1, x2)) -> c51(A__U13(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U13(U61(z0, z1, z2), x1, x2)) -> c51(A__U13(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U13(U62(z0, z1, z2), 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c52(A__U14(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U14(U14(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U14(U15(z0, z1), x1, x2)) -> c52(A__U14(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U14(U16(z0), x1, x2)) -> c52(A__U14(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U14(U21(z0, z1), x1, x2)) -> c52(A__U14(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U14(U22(z0, z1), x1, x2)) -> c52(A__U14(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U14(U23(z0), x1, x2)) -> c52(A__U14(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U14(U31(z0, z1), x1, x2)) -> c52(A__U14(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U14(U32(z0), x1, x2)) -> c52(A__U14(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U14(U41(z0), x1, x2)) -> c52(A__U14(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U14(U51(z0, z1), x1, x2)) -> c52(A__U14(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U14(U52(z0, z1), x1, x2)) -> c52(A__U14(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U14(U61(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U14(U62(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U14(U63(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U14(U64(z0, z1, z2), x1, x2)) -> c52(A__U14(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U14(plus(z0, z1), x1, x2)) -> c52(A__U14(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U14(tt, x1, x2)) -> c52(A__U14(tt, x1, x2)) MARK(U14(s(z0), x1, x2)) -> c52(MARK(s(z0))) MARK(U14(isNatKind(z0), x1, x2)) -> c7(A__U14(a__isNatKind(z0), x1, x2)) MARK(U14(isNatKind(z0), x1, x2)) -> c7(MARK(isNatKind(z0))) MARK(U14(isNat(z0), x1, x2)) -> c7(A__U14(a__isNat(z0), x1, x2)) MARK(U14(isNat(z0), x1, x2)) -> c7(MARK(isNat(z0))) MARK(U15(U11(z0, z1, z2), x1)) -> 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MARK(U41(z0))) MARK(U15(U51(z0, z1), x1)) -> c53(A__U15(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U15(U52(z0, z1), x1)) -> c53(A__U15(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U15(U61(z0, z1, z2), x1)) -> c53(A__U15(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U15(U62(z0, z1, z2), x1)) -> c53(A__U15(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U15(U63(z0, z1, z2), x1)) -> c53(A__U15(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U15(U64(z0, z1, z2), x1)) -> c53(A__U15(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U15(plus(z0, z1), x1)) -> c53(A__U15(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U15(tt, x1)) -> c53(A__U15(tt, x1)) MARK(U15(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U15(isNatKind(z0), x1)) -> c9(A__U15(a__isNatKind(z0), x1)) MARK(U15(isNatKind(z0), x1)) -> c9(MARK(isNatKind(z0))) MARK(U15(isNat(z0), x1)) -> c9(A__U15(a__isNat(z0), x1)) MARK(U15(isNat(z0), x1)) -> c9(MARK(isNat(z0))) MARK(U21(U11(z0, z1, z2), x1)) -> c56(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U21(U12(z0, z1, z2), x1)) -> c56(A__U21(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U21(U13(z0, z1, z2), x1)) -> c56(A__U21(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U21(U14(z0, z1, z2), x1)) -> c56(A__U21(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U21(U15(z0, z1), x1)) -> c56(A__U21(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U21(U16(z0), x1)) -> c56(A__U21(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0, z1), x1)) -> c56(A__U21(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U21(U23(z0), x1)) -> c56(A__U21(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0), x1)) -> c56(A__U21(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U21(U51(z0, z1), x1)) -> c56(A__U21(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U61(z0, z1, z2), x1)) -> c56(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1, z2), x1)) -> c56(A__U21(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U21(U63(z0, z1, z2), x1)) -> c56(A__U21(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U21(U64(z0, z1, z2), x1)) -> c56(A__U21(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U21(plus(z0, z1), x1)) -> c56(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U21(isNatKind(z0), x1)) -> c10(A__U21(a__isNatKind(z0), x1)) MARK(U21(isNatKind(z0), x1)) -> c10(MARK(isNatKind(z0))) MARK(U21(isNat(z0), x1)) -> c10(A__U21(a__isNat(z0), x1)) MARK(U21(isNat(z0), 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MARK(U22(U41(z0), x1)) -> c57(A__U22(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U22(U51(z0, z1), x1)) -> c57(A__U22(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U22(U52(z0, z1), x1)) -> c57(A__U22(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U22(U61(z0, z1, z2), x1)) -> c57(A__U22(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U22(U62(z0, z1, z2), x1)) -> c57(A__U22(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U22(U63(z0, z1, z2), x1)) -> c57(A__U22(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U22(U64(z0, z1, z2), x1)) -> c57(A__U22(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U22(plus(z0, z1), x1)) -> c57(A__U22(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U22(tt, x1)) -> c57(A__U22(tt, x1)) MARK(U22(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U22(isNatKind(z0), x1)) -> c11(A__U22(a__isNatKind(z0), x1)) MARK(U22(isNatKind(z0), x1)) -> c11(MARK(isNatKind(z0))) MARK(U22(isNat(z0), x1)) -> c11(A__U22(a__isNat(z0), x1)) MARK(U22(isNat(z0), x1)) -> c11(MARK(isNat(z0))) MARK(U31(U11(z0, z1, z2), x1)) -> c59(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U31(U12(z0, z1, z2), x1)) -> c59(A__U31(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U31(U13(z0, z1, z2), x1)) -> c59(A__U31(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U31(U14(z0, z1, z2), x1)) -> c59(A__U31(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U31(U15(z0, z1), x1)) -> c59(A__U31(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U31(U16(z0), x1)) -> c59(A__U31(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0, z1), x1)) -> c59(A__U31(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U31(U23(z0), x1)) -> c59(A__U31(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0), x1)) -> c59(A__U31(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U31(U51(z0, z1), x1)) -> c59(A__U31(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U61(z0, z1, z2), x1)) -> c59(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1, z2), x1)) -> c59(A__U31(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U31(U63(z0, z1, z2), x1)) -> c59(A__U31(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U31(U64(z0, z1, z2), x1)) -> c59(A__U31(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c59(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U31(isNatKind(z0), x1)) -> c13(A__U31(a__isNatKind(z0), x1)) MARK(U31(isNatKind(z0), x1)) -> c13(MARK(isNatKind(z0))) MARK(U31(isNat(z0), x1)) -> c13(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c13(MARK(isNat(z0))) MARK(U51(U11(z0, z1, z2), x1)) -> c62(A__U51(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U51(U12(z0, z1, z2), x1)) -> c62(A__U51(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U51(isNatKind(z0), x1)) -> c62(A__U51(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U51(U13(z0, z1, z2), x1)) -> c62(A__U51(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U51(U14(z0, z1, z2), x1)) -> c62(A__U51(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U51(U15(z0, z1), x1)) -> c62(A__U51(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U51(isNat(z0), x1)) -> c62(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(U16(z0), x1)) -> c62(A__U51(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U51(U21(z0, z1), x1)) -> c62(A__U51(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U51(U22(z0, z1), x1)) -> c62(A__U51(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U51(U23(z0), x1)) -> c62(A__U51(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U51(U31(z0, z1), x1)) -> c62(A__U51(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1)) -> c62(A__U51(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U51(U41(z0), x1)) -> c62(A__U51(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U51(U51(z0, z1), x1)) -> c62(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0, z1), x1)) -> c62(A__U51(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U51(U61(z0, z1, z2), x1)) -> c62(A__U51(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1, z2), x1)) -> c62(A__U51(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U51(U63(z0, z1, z2), x1)) -> c62(A__U51(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U51(U64(z0, z1, z2), x1)) -> c62(A__U51(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U51(plus(z0, z1), x1)) -> c62(A__U51(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U51(tt, x1)) -> c62(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U52(U11(z0, z1, z2), x1)) -> c63(A__U52(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2))) MARK(U52(U12(z0, z1, z2), x1)) -> c63(A__U52(a__U12(mark(z0), z1, z2), x1), MARK(U12(z0, z1, z2))) MARK(U52(isNatKind(z0), x1)) -> c63(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(U13(z0, z1, z2), x1)) -> c63(A__U52(a__U13(mark(z0), z1, z2), x1), MARK(U13(z0, z1, z2))) MARK(U52(U14(z0, z1, z2), x1)) -> c63(A__U52(a__U14(mark(z0), z1, z2), x1), MARK(U14(z0, z1, z2))) MARK(U52(U15(z0, z1), x1)) -> c63(A__U52(a__U15(mark(z0), z1), x1), MARK(U15(z0, z1))) MARK(U52(isNat(z0), x1)) -> c63(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U16(z0), x1)) -> c63(A__U52(a__U16(mark(z0)), x1), MARK(U16(z0))) MARK(U52(U21(z0, z1), x1)) -> c63(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0, z1), x1)) -> c63(A__U52(a__U22(mark(z0), z1), x1), MARK(U22(z0, z1))) MARK(U52(U23(z0), x1)) -> c63(A__U52(a__U23(mark(z0)), x1), MARK(U23(z0))) MARK(U52(U31(z0, z1), x1)) -> c63(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c63(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0), x1)) -> c63(A__U52(a__U41(mark(z0)), x1), MARK(U41(z0))) MARK(U52(U51(z0, z1), x1)) -> c63(A__U52(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U52(U52(z0, z1), x1)) -> c63(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U61(z0, z1, z2), x1)) -> c63(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1, z2), x1)) -> c63(A__U52(a__U62(mark(z0), z1, z2), x1), MARK(U62(z0, z1, z2))) MARK(U52(U63(z0, z1, z2), x1)) -> c63(A__U52(a__U63(mark(z0), z1, z2), x1), MARK(U63(z0, z1, z2))) MARK(U52(U64(z0, z1, z2), x1)) -> c63(A__U52(a__U64(mark(z0), z1, z2), x1), MARK(U64(z0, z1, z2))) MARK(U52(plus(z0, z1), x1)) -> c63(A__U52(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U52(tt, x1)) -> c63(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c63(MARK(s(z0))) MARK(U61(U11(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U61(U12(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U61(isNatKind(z0), x1, x2)) -> c64(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(U13(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U61(U14(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U61(U15(z0, z1), x1, x2)) -> c64(A__U61(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U61(isNat(z0), x1, x2)) -> c64(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U16(z0), x1, x2)) -> c64(A__U61(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c64(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0, z1), x1, x2)) -> c64(A__U61(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U61(U23(z0), x1, x2)) -> c64(A__U61(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c64(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c64(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0), x1, x2)) -> c64(A__U61(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U61(U51(z0, z1), x1, x2)) -> c64(A__U61(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U61(U52(z0, z1), x1, x2)) -> c64(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U61(U63(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U61(U64(z0, z1, z2), x1, x2)) -> c64(A__U61(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U61(plus(z0, z1), x1, x2)) -> c64(A__U61(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U61(tt, x1, x2)) -> c64(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c64(MARK(s(z0))) MARK(U62(U11(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U62(U12(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U62(isNatKind(z0), x1, x2)) -> c65(A__U62(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U62(U13(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U62(U14(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U62(U15(z0, z1), x1, x2)) -> c65(A__U62(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U62(isNat(z0), x1, x2)) -> c65(A__U62(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U62(U16(z0), x1, x2)) -> c65(A__U62(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U62(U21(z0, z1), x1, x2)) -> c65(A__U62(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U62(U22(z0, z1), x1, x2)) -> c65(A__U62(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U62(U23(z0), x1, x2)) -> c65(A__U62(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U62(U31(z0, z1), x1, x2)) -> c65(A__U62(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1, x2)) -> c65(A__U62(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U62(U41(z0), x1, x2)) -> c65(A__U62(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U62(U51(z0, z1), x1, x2)) -> c65(A__U62(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U62(U52(z0, z1), x1, x2)) -> c65(A__U62(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U62(U61(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U62(U63(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U62(U64(z0, z1, z2), x1, x2)) -> c65(A__U62(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U62(plus(z0, z1), x1, x2)) -> c65(A__U62(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U62(tt, x1, x2)) -> c65(A__U62(tt, x1, x2)) MARK(U62(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U63(U11(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U63(U12(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U63(isNatKind(z0), x1, x2)) -> c66(A__U63(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U63(U13(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U63(U14(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U63(U15(z0, z1), x1, x2)) -> c66(A__U63(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U63(isNat(z0), x1, x2)) -> c66(A__U63(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U63(U16(z0), x1, x2)) -> c66(A__U63(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U63(U21(z0, z1), x1, x2)) -> c66(A__U63(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U63(U22(z0, z1), x1, x2)) -> c66(A__U63(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U63(U23(z0), x1, x2)) -> c66(A__U63(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U63(U31(z0, z1), x1, x2)) -> c66(A__U63(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U63(U32(z0), x1, x2)) -> c66(A__U63(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U63(U41(z0), x1, x2)) -> c66(A__U63(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U63(U51(z0, z1), x1, x2)) -> c66(A__U63(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U63(U52(z0, z1), x1, x2)) -> c66(A__U63(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U63(U61(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U63(U62(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U63(U63(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U63(U64(z0, z1, z2), x1, x2)) -> c66(A__U63(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U63(plus(z0, z1), x1, x2)) -> c66(A__U63(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U63(tt, x1, x2)) -> c66(A__U63(tt, x1, x2)) MARK(U63(s(z0), x1, x2)) -> c66(MARK(s(z0))) MARK(U64(U11(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2))) MARK(U64(U12(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2))) MARK(U64(isNatKind(z0), x1, x2)) -> c67(A__U64(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U64(U13(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U13(mark(z0), z1, z2), x1, x2), MARK(U13(z0, z1, z2))) MARK(U64(U14(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U14(mark(z0), z1, z2), x1, x2), MARK(U14(z0, z1, z2))) MARK(U64(U15(z0, z1), x1, x2)) -> c67(A__U64(a__U15(mark(z0), z1), x1, x2), MARK(U15(z0, z1))) MARK(U64(isNat(z0), x1, x2)) -> c67(A__U64(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U64(U16(z0), x1, x2)) -> c67(A__U64(a__U16(mark(z0)), x1, x2), MARK(U16(z0))) MARK(U64(U21(z0, z1), x1, x2)) -> c67(A__U64(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U64(U22(z0, z1), x1, x2)) -> c67(A__U64(a__U22(mark(z0), z1), x1, x2), MARK(U22(z0, z1))) MARK(U64(U23(z0), x1, x2)) -> c67(A__U64(a__U23(mark(z0)), x1, x2), MARK(U23(z0))) MARK(U64(U31(z0, z1), x1, x2)) -> c67(A__U64(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U64(U32(z0), x1, x2)) -> c67(A__U64(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U64(U41(z0), x1, x2)) -> c67(A__U64(a__U41(mark(z0)), x1, x2), MARK(U41(z0))) MARK(U64(U51(z0, z1), x1, x2)) -> c67(A__U64(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U64(U52(z0, z1), x1, x2)) -> c67(A__U64(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U64(U61(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U64(U62(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U62(mark(z0), z1, z2), x1, x2), MARK(U62(z0, z1, z2))) MARK(U64(U63(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U63(mark(z0), z1, z2), x1, x2), MARK(U63(z0, z1, z2))) MARK(U64(U64(z0, z1, z2), x1, x2)) -> c67(A__U64(a__U64(mark(z0), z1, z2), x1, x2), MARK(U64(z0, z1, z2))) MARK(U64(plus(z0, z1), x1, x2)) -> c67(A__U64(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U64(tt, x1, x2)) -> c67(A__U64(tt, x1, x2)) MARK(U64(s(z0), x1, x2)) -> c67(MARK(s(z0))) MARK(plus(x0, U11(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U12(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, isNatKind(z0))) -> c68(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(plus(x0, U13(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U14(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U15(z0, z1))) -> c68(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c68(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U16(z0))) -> c68(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(x0)) MARK(plus(x0, U21(z0, z1))) -> c68(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U22(z0, z1))) -> c68(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U23(z0))) -> c68(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c68(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c68(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0))) -> c68(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(x0)) MARK(plus(x0, U51(z0, z1))) -> c68(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U52(z0, z1))) -> c68(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U61(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U62(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U63(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U64(z0, z1, z2))) -> c68(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c68(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c68(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c68(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1, z2), x1)) -> c68(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2))) MARK(plus(U12(z0, z1, z2), x1)) -> c68(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2))) MARK(plus(isNatKind(z0), x1)) -> c68(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(plus(U13(z0, z1, z2), x1)) -> c68(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(U13(z0, z1, z2))) MARK(plus(U14(z0, z1, z2), x1)) -> c68(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(U14(z0, z1, z2))) MARK(plus(U15(z0, z1), x1)) -> c68(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(U15(z0, z1))) MARK(plus(isNat(z0), x1)) -> c68(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U16(z0), x1)) -> c68(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(U16(z0))) MARK(plus(U21(z0, z1), x1)) -> c68(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(plus(U22(z0, z1), x1)) -> c68(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(U22(z0, z1))) MARK(plus(U23(z0), x1)) -> c68(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(U23(z0))) MARK(plus(U31(z0, z1), x1)) -> c68(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c68(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0), x1)) -> c68(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(U41(z0))) MARK(plus(U51(z0, z1), x1)) -> c68(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(plus(U52(z0, z1), x1)) -> c68(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(plus(U61(z0, z1, z2), x1)) -> c68(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(plus(U62(z0, z1, z2), x1)) -> c68(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(U62(z0, z1, z2))) MARK(plus(U63(z0, z1, z2), x1)) -> c68(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(U63(z0, z1, z2))) MARK(plus(U64(z0, z1, z2), x1)) -> c68(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(U64(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c68(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c68(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c68(MARK(x0)) MARK(plus(tt, x1)) -> c68(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c68(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) MARK(plus(x0, U12(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) MARK(plus(x0, isNatKind(z0))) -> c69(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(plus(x0, U13(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U13(mark(z0), z1, z2)), MARK(U13(z0, z1, z2))) MARK(plus(x0, U14(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U14(mark(z0), z1, z2)), MARK(U14(z0, z1, z2))) MARK(plus(x0, U15(z0, z1))) -> c69(A__PLUS(mark(x0), a__U15(mark(z0), z1)), MARK(U15(z0, z1))) MARK(plus(x0, isNat(z0))) -> c69(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U16(z0))) -> c69(A__PLUS(mark(x0), a__U16(mark(z0))), MARK(U16(z0))) MARK(plus(x0, U21(z0, z1))) -> c69(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(plus(x0, U22(z0, z1))) -> c69(A__PLUS(mark(x0), a__U22(mark(z0), z1)), MARK(U22(z0, z1))) MARK(plus(x0, U23(z0))) -> c69(A__PLUS(mark(x0), a__U23(mark(z0))), MARK(U23(z0))) MARK(plus(x0, U31(z0, z1))) -> c69(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c69(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0))) -> c69(A__PLUS(mark(x0), a__U41(mark(z0))), MARK(U41(z0))) MARK(plus(x0, U51(z0, z1))) -> c69(A__PLUS(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(plus(x0, U52(z0, z1))) -> c69(A__PLUS(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(plus(x0, U61(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(plus(x0, U62(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U62(mark(z0), z1, z2)), MARK(U62(z0, z1, z2))) MARK(plus(x0, U63(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U63(mark(z0), z1, z2)), MARK(U63(z0, z1, z2))) MARK(plus(x0, U64(z0, z1, z2))) -> c69(A__PLUS(mark(x0), a__U64(mark(z0), z1, z2)), MARK(U64(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c69(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c69(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1, z2), x1)) -> c69(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U12(z0, z1, z2), x1)) -> c69(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(isNatKind(z0), x1)) -> c69(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(plus(U13(z0, z1, z2), x1)) -> c69(A__PLUS(a__U13(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U14(z0, z1, z2), x1)) -> c69(A__PLUS(a__U14(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U15(z0, z1), x1)) -> c69(A__PLUS(a__U15(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c69(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U16(z0), x1)) -> c69(A__PLUS(a__U16(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1), x1)) -> c69(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U22(z0, z1), x1)) -> c69(A__PLUS(a__U22(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U23(z0), x1)) -> c69(A__PLUS(a__U23(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c69(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c69(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0), x1)) -> c69(A__PLUS(a__U41(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1), x1)) -> c69(A__PLUS(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1), x1)) -> c69(A__PLUS(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U61(z0, z1, z2), x1)) -> c69(A__PLUS(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U62(z0, z1, z2), x1)) -> c69(A__PLUS(a__U62(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U63(z0, z1, z2), x1)) -> c69(A__PLUS(a__U63(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U64(z0, z1, z2), x1)) -> c69(A__PLUS(a__U64(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c69(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c69(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c69(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c69(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c69(A__PLUS(mark(x0), 0)) A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U31(tt, x1), plus(0, x1), x2), A__ISNATKIND(plus(0, x1))) A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U31(a__U31(a__isNatKind(z0), z1), x1), plus(plus(z0, z1), x1), x2), A__ISNATKIND(plus(plus(z0, z1), x1))) A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U31(a__U41(a__isNatKind(z0)), x1), plus(s(z0), x1), x2), A__ISNATKIND(plus(s(z0), x1))) A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U31(isNatKind(z0), x1), plus(z0, x1), x2), A__ISNATKIND(plus(z0, x1))) A__U11(tt, plus(x0, z1), x2) -> c(A__ISNATKIND(plus(x0, z1))) A__U11(tt, s(0), x1) -> c(A__U12(a__U41(tt), s(0), x1), A__ISNATKIND(s(0))) A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U41(a__U31(a__isNatKind(z0), z1)), s(plus(z0, z1)), x1), A__ISNATKIND(s(plus(z0, z1)))) A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U41(a__U41(a__isNatKind(z0))), s(s(z0)), x1), A__ISNATKIND(s(s(z0)))) A__U11(tt, s(z0), x1) -> c(A__U12(a__U41(isNatKind(z0)), s(z0), x1), A__ISNATKIND(s(z0))) A__U11(tt, s(x0), x1) -> c(A__ISNATKIND(s(x0))) A__U12(tt, x0, plus(0, x2)) -> c2(A__U13(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__U13(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__U13(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U12(tt, x0, plus(z0, x2)) -> c2(A__U13(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U12(tt, x0, plus(x1, z1)) -> c2(A__ISNATKIND(plus(x1, z1))) A__U12(tt, x0, s(0)) -> c2(A__U13(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__U13(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U12(tt, x0, s(s(z0))) -> c2(A__U13(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U12(tt, x0, s(z0)) -> c2(A__U13(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U12(tt, x0, s(x1)) -> c2(A__ISNATKIND(s(x1))) A__U13(tt, x0, plus(0, x2)) -> c4(A__U14(a__U31(tt, x2), x0, plus(0, x2)), A__ISNATKIND(plus(0, x2))) A__U13(tt, x0, plus(plus(z0, z1), x2)) -> c4(A__U14(a__U31(a__U31(a__isNatKind(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNATKIND(plus(plus(z0, z1), x2))) A__U13(tt, x0, plus(s(z0), x2)) -> c4(A__U14(a__U31(a__U41(a__isNatKind(z0)), x2), x0, plus(s(z0), x2)), A__ISNATKIND(plus(s(z0), x2))) A__U13(tt, x0, plus(z0, x2)) -> c4(A__U14(a__U31(isNatKind(z0), x2), x0, plus(z0, x2)), A__ISNATKIND(plus(z0, x2))) A__U13(tt, x0, plus(x1, z1)) -> c4(A__ISNATKIND(plus(x1, z1))) K tuples:none Defined Rule Symbols: a__U11_3, a__U12_3, a__U13_3, a__U14_3, a__U15_2, a__U16_1, a__U21_2, a__U22_2, a__U23_1, a__U31_2, a__U32_1, a__U41_1, a__U51_2, a__U52_2, a__U61_3, a__U62_3, a__U63_3, a__U64_3, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1 Defined Pair Symbols: A__U52_2, MARK_1, A__U15_2, A__U22_2, A__U31_2, A__ISNATKIND_1, A__U11_3, A__U12_3, A__U13_3, A__U14_3, A__U21_2, A__U51_2, A__U61_3, A__U62_3, A__U63_3, A__U64_3, A__ISNAT_1, A__PLUS_2 Compound Symbols: c26_1, c50_1, c54_1, c71_1, c8_1, c14_1, c18_1, c43_1, c55_1, c58_1, c60_1, c61_1, c_1, c2_1, c4_2, c4_1, c6_2, c6_1, c12_2, c12_1, c24_2, c24_1, c28_2, c28_1, c30_2, c30_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c38_2, c38_1, c39_2, c39_1, c42_2, c42_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c1_1, c49_2, c49_1, c3_1, c51_2, c51_1, c5_1, c52_2, c52_1, c7_1, c53_2, c53_1, c9_1, c56_2, c56_1, c10_1, c57_2, c57_1, c11_1, c59_2, c59_1, c13_1, c62_2, c62_1, c63_2, c63_1, c64_2, c64_1, c65_2, c65_1, c66_2, c66_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c_2, c2_2