KILLED proof of input_QRxIYaNb6W.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 1868 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 412 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 29 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 43 ms] (112) CdtProblem (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (116) CdtProblem (117) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 2 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms] (136) CdtProblem (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 16 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 74 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 9 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 107 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 102 ms] (166) CdtProblem (167) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 102 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 138 ms] (178) CdtProblem (179) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 18 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 113 ms] (184) CdtProblem (185) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 143 ms] (190) CdtProblem (191) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 266 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 28 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 339 ms] (200) CdtProblem (201) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 77 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 28 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (228) 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__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 ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__isNatKind_1 a__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 ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 0, V2) -> a__U12(tt, 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 -> 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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 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 ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__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 ---------------------------------------- (15) 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 ---------------------------------------- (16) 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 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 2 }-> a__U12(a__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 ---------------------------------------- (19) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V1, V2) -> a__U12(a__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 ---------------------------------------- (21) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z', z'') -{ 1 }-> a__U12(a__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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 29 trailing nodes: A__ISNAT(0) -> c37 A__U15(z0, z1) -> c9 A__U41(z0) -> c23 A__U32(z0) -> c21 A__PLUS(z0, z1) -> c47 A__ISNAT(z0) -> c40 A__U62(z0, z1, z2) -> c31 A__U21(z0, z1) -> c13 A__ISNATKIND(0) -> c41 A__U23(tt) -> c16 A__U23(z0) -> c17 A__U61(z0, z1, z2) -> c29 A__U32(tt) -> c20 A__U16(z0) -> c11 A__U14(z0, z1, z2) -> c7 A__U64(z0, z1, z2) -> c36 A__U22(z0, z1) -> c15 A__U13(z0, z1, z2) -> c5 A__U51(z0, z1) -> c25 A__U12(z0, z1, z2) -> c3 A__ISNATKIND(z0) -> c44 A__U41(tt) -> c22 MARK(0) -> c72 A__U16(tt) -> c10 A__U11(z0, z1, z2) -> c1 MARK(tt) -> c70 A__U52(z0, z1) -> c27 A__U31(z0, z1) -> c19 A__U63(z0, z1, z2) -> c33 ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (28) 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 ---------------------------------------- (29) 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)) ---------------------------------------- (30) 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 ---------------------------------------- (31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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 ---------------------------------------- (33) 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)) ---------------------------------------- (34) 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 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (36) 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 ---------------------------------------- (37) 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)) ---------------------------------------- (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__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 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (41) 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)) ---------------------------------------- (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__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 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (44) 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 ---------------------------------------- (45) 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)) ---------------------------------------- (46) 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 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (48) 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 ---------------------------------------- (49) 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)) ---------------------------------------- (50) 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 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (52) 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 ---------------------------------------- (53) 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)) ---------------------------------------- (54) 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 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (56) 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 ---------------------------------------- (57) 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)) ---------------------------------------- (58) 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 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (60) 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 ---------------------------------------- (61) 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)) ---------------------------------------- (62) 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 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (64) 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 ---------------------------------------- (65) 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)) ---------------------------------------- (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__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 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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__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 ---------------------------------------- (69) 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)) ---------------------------------------- (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__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 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U64(tt, tt, x1) -> c35(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (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__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 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (75) 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)) ---------------------------------------- (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__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 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (79) 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)) ---------------------------------------- (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__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 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (83) 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)) ---------------------------------------- (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__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 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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 ---------------------------------------- (87) 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)) ---------------------------------------- (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__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 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (91) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (95) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1, x2)) -> c48(A__U11(0, x1, x2), MARK(0)) ---------------------------------------- (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)) 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 ---------------------------------------- (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)) 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 ---------------------------------------- (101) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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)) 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 ---------------------------------------- (103) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U12(0, x1, x2)) -> c49(A__U12(0, x1, x2), MARK(0)) ---------------------------------------- (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)) 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 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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 ---------------------------------------- (109) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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)) 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 ---------------------------------------- (111) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U13(0, x1, x2)) -> c51(A__U13(0, x1, x2), MARK(0)) ---------------------------------------- (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)) 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 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (117) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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)) 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 ---------------------------------------- (119) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U14(0, x1, x2)) -> c52(A__U14(0, x1, x2), MARK(0)) ---------------------------------------- (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)) 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 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (125) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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)) 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 ---------------------------------------- (127) 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)) ---------------------------------------- (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(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 ---------------------------------------- (129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U15(0, x1)) -> c53(A__U15(0, x1), MARK(0)) ---------------------------------------- (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(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 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (133) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(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 ---------------------------------------- (135) 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)) ---------------------------------------- (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(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 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) ---------------------------------------- (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(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 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (141) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(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 ---------------------------------------- (143) 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)) ---------------------------------------- (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(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 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U22(0, x1)) -> c57(A__U22(0, x1), MARK(0)) ---------------------------------------- (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(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, 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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)) -> 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)) 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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 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (149) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(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, 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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))) 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 ---------------------------------------- (151) 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)) ---------------------------------------- (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(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))) 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, 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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(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)) 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 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) ---------------------------------------- (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(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, 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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(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 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)) -> 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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(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, 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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(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 ---------------------------------------- (157) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(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 ---------------------------------------- (159) 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)) ---------------------------------------- (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(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)) -> 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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(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, 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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(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))) 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 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U51(0, x1)) -> c62(A__U51(0, x1), MARK(0)) ---------------------------------------- (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(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(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, 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(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 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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 ---------------------------------------- (165) 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)) ---------------------------------------- (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(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 ---------------------------------------- (167) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U52(0, x1)) -> c63(A__U52(0, x1), MARK(0)) ---------------------------------------- (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(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, 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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)) -> 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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))) 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)) -> 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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), 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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(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 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (171) 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)) ---------------------------------------- (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(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)) 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 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U61(0, x1, x2)) -> c64(A__U61(0, x1, x2), 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(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))) 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 ---------------------------------------- (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(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))) 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))) 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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), 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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 ---------------------------------------- (177) 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)) ---------------------------------------- (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(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 ---------------------------------------- (179) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U62(0, x1, x2)) -> c65(A__U62(0, x1, x2), 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(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)) -> 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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 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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, 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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(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))) 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, 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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))) 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 ---------------------------------------- (183) 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)) ---------------------------------------- (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(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 ---------------------------------------- (185) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U63(0, x1, x2)) -> c66(A__U63(0, x1, x2), MARK(0)) ---------------------------------------- (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(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))) 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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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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))) 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 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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(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, 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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))) 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 ---------------------------------------- (189) 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)) ---------------------------------------- (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(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, 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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(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 ---------------------------------------- (191) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U64(0, x1, x2)) -> c67(A__U64(0, x1, x2), MARK(0)) ---------------------------------------- (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(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))) 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, 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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(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 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)) -> 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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, 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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)) -> 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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, 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))) 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 ---------------------------------------- (195) 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)) ---------------------------------------- (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(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), 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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)) -> 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, 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, 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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, 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 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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)) -> 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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(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 ---------------------------------------- (199) 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)) ---------------------------------------- (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(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))) 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, 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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), 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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)) 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 ---------------------------------------- (201) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c69(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (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(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), 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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(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, 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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, 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 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0, z1) -> a__U12(a__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, 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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)) 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), 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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)) 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 ---------------------------------------- (205) 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))) ---------------------------------------- (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(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), 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(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, 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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, 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 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) -> 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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(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)) -> 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))) 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 ---------------------------------------- (209) 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))) ---------------------------------------- (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(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))) 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 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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)) -> 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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)) 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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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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, 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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), 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))) 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 ---------------------------------------- (213) 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))) ---------------------------------------- (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(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, 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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))) 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, 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(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 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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), 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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, 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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, 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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))) 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 ---------------------------------------- (217) 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))) ---------------------------------------- (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(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), 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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))) 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)) -> 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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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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)) 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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 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) -> 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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), 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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)) 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))) 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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(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))) 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 ---------------------------------------- (221) 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))) ---------------------------------------- (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(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, 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(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 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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, 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))) 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), 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))) 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 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(a__isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) by A__U13(tt, x0, s(x1)) -> c4(A__U14(U41(a__isNatKind(x1)), x0, s(x1)), A__ISNATKIND(s(x1))) A__U13(tt, x0, s(0)) -> c4(A__U14(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U13(tt, x0, s(plus(z0, z1))) -> c4(A__U14(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U13(tt, x0, s(s(z0))) -> c4(A__U14(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) ---------------------------------------- (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(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, 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(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))) A__U13(tt, x0, s(x1)) -> c4(A__U14(U41(a__isNatKind(x1)), x0, s(x1)), A__ISNATKIND(s(x1))) A__U13(tt, x0, s(0)) -> c4(A__U14(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U13(tt, x0, s(plus(z0, z1))) -> c4(A__U14(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U13(tt, x0, s(s(z0))) -> c4(A__U14(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U13(tt, x0, s(z0)) -> c4(A__U14(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, 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))) A__U13(tt, x0, s(x1)) -> c4(A__U14(U41(a__isNatKind(x1)), x0, s(x1)), A__ISNATKIND(s(x1))) A__U13(tt, x0, s(0)) -> c4(A__U14(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U13(tt, x0, s(plus(z0, z1))) -> c4(A__U14(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U13(tt, x0, s(s(z0))) -> c4(A__U14(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U13(tt, x0, s(z0)) -> c4(A__U14(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_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, c4_2 ---------------------------------------- (227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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, 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))) 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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), 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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(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))) A__U13(tt, x0, s(0)) -> c4(A__U14(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U13(tt, x0, s(plus(z0, z1))) -> c4(A__U14(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U13(tt, x0, s(s(z0))) -> c4(A__U14(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, s(x1)) -> c4(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, 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, 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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))) A__U13(tt, x0, s(0)) -> c4(A__U14(a__U41(tt), x0, s(0)), A__ISNATKIND(s(0))) A__U13(tt, x0, s(plus(z0, z1))) -> c4(A__U14(a__U41(a__U31(a__isNatKind(z0), z1)), x0, s(plus(z0, z1))), A__ISNATKIND(s(plus(z0, z1)))) A__U13(tt, x0, s(s(z0))) -> c4(A__U14(a__U41(a__U41(a__isNatKind(z0))), x0, s(s(z0))), A__ISNATKIND(s(s(z0)))) A__U13(tt, x0, s(z0)) -> c4(A__U14(a__U41(isNatKind(z0)), x0, s(z0)), A__ISNATKIND(s(z0))) A__U13(tt, x0, s(x1)) -> c4(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_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, c4_2